U.S. patent application number 13/660732 was filed with the patent office on 2013-04-25 for method for designing an electronic circuit.
The applicant listed for this patent is Christoph BROMBERGER. Invention is credited to Christoph BROMBERGER.
Application Number | 20130099874 13/660732 |
Document ID | / |
Family ID | 44118730 |
Filed Date | 2013-04-25 |
United States Patent
Application |
20130099874 |
Kind Code |
A1 |
BROMBERGER; Christoph |
April 25, 2013 |
METHOD FOR DESIGNING AN ELECTRONIC CIRCUIT
Abstract
An electronic circuit and method for designing an electronic
circuit is provided that includes a first source element, a second
source element, a first matching network, and a second matching
network. The first matching network and the second matching network
are designed by means of a method using the Poincare distance, in
which the second source element is designed to output a signal with
a center frequency, in which the load has a load impedance, in
which the second matching network has line-like series elements
that carry the signal. The line-like series elements only have line
impedances less than the load impedance or a sum of the electrical
lengths of the line-like series elements, each of which has a line
impedance greater than the load impedance, is less than one quarter
of a wavelength associated with the signal.
Inventors: |
BROMBERGER; Christoph;
(Blaustein, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
BROMBERGER; Christoph |
Blaustein |
|
DE |
|
|
Family ID: |
44118730 |
Appl. No.: |
13/660732 |
Filed: |
October 25, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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PCT/EP2011/002074 |
Apr 24, 2011 |
|
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13660732 |
|
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Current U.S.
Class: |
333/32 ; 716/115;
716/129; 716/133 |
Current CPC
Class: |
G06F 30/394 20200101;
H03H 2260/00 20130101; H03H 7/38 20130101; H03F 3/60 20130101; H03F
1/56 20130101; H03F 2200/387 20130101; H03F 1/0288 20130101 |
Class at
Publication: |
333/32 ; 716/115;
716/133; 716/129 |
International
Class: |
G06F 17/50 20060101
G06F017/50; H03H 7/38 20060101 H03H007/38 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 25, 2010 |
DE |
DE102010018274.5 |
Claims
1. A method for designing an electronic circuit, the method
comprising: providing the circuit with a first matching network
with a first connection and a second connection; connecting a load
of the circuit to the first connection, wherein a first load
reflection factor that depends on the load is achieved at the first
connection; connecting a source element of the circuit with a first
source reflection factor to the second connection, wherein a
transformed first load reflection factor into the second connection
and a transformed first source reflection factor into the first
connection are achieved via the first matching network; determining
for each first distance from among a number of first distances a
first circle as a set of all points at a first distance from a
complex conjugate of the first load reflection factor by: P ( y , a
on * ) = arc tan h ( y - a on * 1 - y * a on * ) .ident. P R ,
##EQU00043## wherein y is a point on the first circle, y* is the
complex conjugate of the point on the first circle, a.sub.on* is
the complex conjugate of the first load reflection factor, and
P.sub.R is the first distance; determining a second circle as the
set of all points at a first distance from the complex conjugate of
the first source reflection factor by: P ( x , b on * ) = arctanh (
x - b on * 1 - x * b on * ) .ident. P R , ##EQU00044## wherein x is
a point on the second circle, x* is the complex conjugate of the
point on the second circle, b.sub.on* is the complex conjugate of
the first source reflection factor, and P.sub.R is the first
distance; determining a number of first point pairs, wherein a
first pair point of each point pair is on the first circle, and
wherein a second pair point of each point pair is on the second
circle; determining a value of a first parameter for each first
point pair with the first pair point equal to a value of the
transformed first source reflection factor and with the second pair
point equal to a value of the transformed first load reflection
factor; determining an optimum of the first parameter from all
values of the first parameter that are associated with the first
point pairs; determining a first value pair from among the first
point pairs, wherein the optimum is associated with the first value
pair; setting a first value of the transformed first source
reflection factor equal to a first value point of the first value
pair; setting a second value of the transformed first load
reflection factor equal to a second value point of the first value
pair; and determining the first matching network using the first
value of the transformed first source reflection factor, the second
value of the transformed first load reflection factor, the first
source reflection factor, and the first load reflection factor.
2. The method according to claim 1, further comprising: determining
a first function that describes the transforming action of the
first matching network in a forward direction, wherein the first
function is defined by: f a on , a on ' , .PHI. ( z 1 ) = .PHI. z 1
- z 0 1 - z 0 * z 1 with ##EQU00045## z 0 = 1 - a on 2 a on 2 a on
' 2 - 1 a on ' - .PHI. - 1 - a on ' 2 a on 2 a on ' 2 - 1 a on ,
##EQU00045.2## wherein a.sub.on is the first load reflection
factor, a.sub.on' is the transformed first load reflection factor,
.phi..epsilon.[0 . . . 2.tau.[ is a parameter, i=2 {square root
over (-1)}, and z.sub.1 is a first argument of the first function;
determining a second function that describes the transforming
action of the first matching network in a reverse direction,
wherein the second function is defined by: f a on , a on ' , .PHI.
R ( z 2 ) = .PHI. z 2 - z 0 R 1 - z 0 R * z 2 with ##EQU00046## z 0
R = 1 - a on ' * 2 a on ' * 2 a on * 2 - 1 a on * - .PHI. - 1 - a
on * 2 a on ' * 2 a on * 2 - 1 a on ' * , ##EQU00046.2## wherein
a.sub.on is the first load reflection factor, a.sub.on* is the
complex conjugate of the first load reflection factor, a.sub.on' is
the transformed first load reflection factor, a.sub.on'* is the
complex conjugate of the transformed first load reflection factor,
.phi..epsilon.[0 . . . 2.tau.[ is the parameter, and z.sub.2 is a
second argument of the second function.
3. The method according to claim 2, further comprising: determining
a value of the parameter for an optimum of the first parameter,
wherein a number of first distances is equal to one, and the first
distance between the transformed first load reflection factor and
the complex conjugate of the first source reflection factor is
determined by: P a on ' , b on * = arc tanh ( a on ' - b on * 1 - b
on * a on ' * ) .ident. P R , ##EQU00047## wherein b.sub.on is the
first source reflection factor, b.sub.on* is the complex conjugate
of the first source reflection factor, a.sub.on' is the transformed
first load reflection factor, and P.sub.R is the first distance),
wherein the value of the parameter is determined when the second
function with the first source reflection factor as its second
argument assumes the first value of the transformed first source
reflection factor as the function value, and determining the first
matching network using the first function for the value of the
parameter.
4. The method according to claim 1, wherein the first parameter is
a mismatch between the transformed first source reflection factor
and the first load reflection factor.
5. The method according to claim 1, wherein a predetermined
mismatch between the transformed first source reflection factor and
the first load reflection factor is a part of the first parameter
as a boundary condition.
6. A method for designing an electronic circuit, the method
comprising: providing a second matching network with a third
connection and a fourth connection; connecting to the third
connection, a variable load with a first operating state and a
second operating state, wherein a second load reflection factor at
the third connection is achieved in the second operating state and
a third load reflection factor is achieved in the first operating
state, and wherein a transformed second load reflection factor into
the fourth connection in the second operating state and a
transformed third load reflection factor in the first operating
state are achieved via the second matching network; determining a
third distance between the transformed second load reflection
factor and the transformed third load reflection factor by: P 3 =
arc tanh ( c off ' - c on ' 1 - c off ' * c on ' ) , ##EQU00048##
wherein c.sub.on' is the transformed second load reflection factor,
c.sub.off' is the transformed third load reflection factor,
c.sub.off'* is the complex conjugate of the transformed third load
reflection factor, and P.sub.3 is the third distance; determining a
third circle as the set of all points at the third distance from
the second load reflection factor by: P ( z , c on ) = arc tanh ( z
- c on 1 - z * c on ) .ident. P 3 , ##EQU00049## wherein z is a
point on the third circle, z* is the complex conjugate of the point
on the third circle, c.sub.on is the second load reflection factor,
c.sub.on* is the complex conjugate of the second load reflection
factor, and P.sub.3 is the third distance; determining a number of
second point pairs, wherein a second pair point of each second
point pair is a point on the third circle; determining a value of a
second parameter for each second point pair, wherein a value of the
third load reflection factor is equal to the second pair point, and
wherein a value of the second load reflection factor is equal to
the first pair point; determining an optimum of the second
parameter from all values of the second parameter that are
associated with the second point pairs; determining a second point
pair associated with the optimum; setting the third value of the
third load reflection factor equal to a second pair point
associated with the optimum of the second point pair associated
with the optimum; setting the fourth value of the second load
reflection factor equal to a first pair point associated with the
optimum of the second point pair associated with the optimum; and
determining the second matching network using the third value of
the third load reflection factor, the fourth value of the second
load reflection factor, the transformed second load reflection
factor), and the transformed third load reflection factor.
7. A method for designing an electronic circuit, the method
comprising: providing the circuit with a first operating state and
a second operating state; providing the circuit with a first source
element with a first source output and a second source element with
a second source output, the first source element having a first
source reflection factor into the first source output in the first
operating state; providing the circuit with a load via a load
input, the load having a load input reflection factor into the load
input; providing the circuit with a T-section with a first input, a
second input, and an output, the load input being connectable to
the output of the T-section, the T-section having a first load
reflection factor into the first input in the second operating
state, the T-section having a second load reflection factor into
the second input in the first operating state, the T-section having
a third load reflection factor into the second input in the second
operating state; providing the circuit with a first matching
network having a first connection and a second connection, the
first connection being connectable to the first input of the
T-section, the second connection being connectable to the first
source output, the first matching network having a transformed
first source reflection factor into the first connection in the
first operating state, the first matching network having a
transformed first load reflection factor into the second connection
in the second operating state; providing the circuit with a second
matching network having a third connection and a fourth connection,
the third connection being connectable to the second input of the
T-section, the fourth connection being connectable to the second
source output, the second matching network having a transformed
second load reflection factor into the fourth connection in the
first operating state, the second matching network having a
transformed third load reflection factor into the fourth connection
in the second operating state; determining a first value of the
transformed first load reflection factor for optimizing a parameter
of the circuit by measurement in the second operating state;
determining a second value of the transformed second load
reflection factor for optimizing the parameter of the circuit by
measurement in the first operating state; determining a third value
of the transformed third load reflection factor for optimizing the
parameter of the circuit by measurement in the second operating
state, wherein the first load reflection factor is set to a first
initial value and the second load reflection factor is set to a
second initial value; calculating a first distance between the
first value and the complex conjugate of the first source
reflection factor by: P 1 = arc tanh ( a on opt ' - b off * 1 - b
off * a on opt ' * ) , ##EQU00050## wherein b.sub.off is the first
source reflection factor, b.sub.off* is the complex conjugate of
the first source reflection factor, a.sub.on'.sub.opt is the first
value of the transformed first load reflection factor, and P.sub.1
is the first distance; determining a first circle as a set of all
points at a first distance from the complex conjugate of the first
load reflection factor by: P ( y , a on * ) = arc tanh ( y - a on *
1 - y * a on * ) .ident. P 1 , ##EQU00051## wherein y is a point on
the first circle, y* is the complex conjugate of the point on the
first circle, a.sub.on* is the complex conjugate of the first load
reflection factor, and P.sub.1 is the first distance; determining a
third distances between the second value and the third value by: P
3 = arc tanh ( c on opt ' - c off opt ' 1 - c on opt ' * c off opt
' ) , ##EQU00052## wherein c.sub.off'.sub.opt is the second value
of the transformed second load reflection factor, c.sub.on'.sub.opt
is the third value of the transformed third load reflection factor,
c.sub.on'.sub.opt* is the complex conjugate of the third value of
the transformed third load reflection factor; determining a third
circle as the set of all points at the third distance from the
third load reflection factor by: P ( z , c on ) = arc tanh ( z - c
on 1 - z * c on ) .ident. P 3 , ##EQU00053## wherein z is a point
on the third circle, z* is the complex conjugate of the point on
the third circle, c.sub.on is the third load reflection factor,
c.sub.on* is the complex conjugate of the third load reflection
factor, and P.sub.3 is the third distance, determining a modified
first circle, wherein the modified first circle is determined as
the set of all modified reflection factors, wherein an overall
impedance is associated with each of the modified reflection
factors, wherein each overall impedance is determined from a first
parallel circuit of a load impedance of the load and an impedance
associated with a reflection factor on the first circle, and
wherein the load impedance is associated with the load input
reflection factor of the load; determining at least one fourth
value of the second load reflection factor, wherein a sum of
squares of the distances between the fourth value and the third
circle and between the fourth value and the modified first circle
is minimized for the at least one fourth value; determining a fifth
value of the transformed first source reflection factor for each
fourth value of the second load reflection factor, wherein a fourth
impedance is determined, wherein the fourth impedance is associated
with the fourth value of the second load reflection factor, wherein
a fifth impedance is determined so that a second parallel circuit
of the fifth impedance with the load impedance is equal to the
fourth impedance, and wherein the fifth value of the transformed
first source reflection factor is associated with the fifth
impedance; determining the first matching network using the first
load reflection factor, the first value of the transformed first
load reflection factor, the first source reflection factor, and the
fifth value of the of the transformed first source reflection
factor; and determining the second matching network using the
second value of the transformed second load reflection factor, the
third value of the transformed third load reflection factor, the
third load reflection factor, and the fourth value of the second
load reflection factor.
8. A method for designing an electronic circuit, the method
comprising: determining a distance value and a third value of a
transformed first load reflection factor, and a fourth value of a
transformed second load reflection factor wherein a first distance
between a first value and the transformed first load reflection
factor is defined by: P 1 = arc tanh ( a opt ' - a ' 1 - a ' * a
opt ' ) , ##EQU00054## wherein a second distance between a second
value and a transformed second load reflection factor is defined
by: P 2 = arc tanh ( c opt ' - c ' 1 - c ' * c opt ' ) ,
##EQU00055## wherein a third distance between the transformed first
load reflection factor and the complex conjugate of the first
source reflection factor is defined by: P 3 = arc tanh ( a ' - b *
1 - ba ' ) , ##EQU00056## wherein a fourth distance between the
transformed second load reflection factor and the complex conjugate
of the second source reflection factor is defined by: P 4 = arc
tanh ( c ' - d * 1 - d c ' ) , ##EQU00057## defining the distance
value, the third value, and the fourth value; determining a fifth
value of the transformed first source reflection factor and a sixth
value of the transformed second source reflection factor, wherein a
first circle with a real center point is determined that intersects
a real reflection factor value of one third and a real reflection
factor value of minus one, and wherein a second circle as the set
of all points with a distance from the real reflection factor value
of one third equal to the distance value is determined by: P ( y ,
1 3 ) = arc tanh ( y - 1 3 1 - y 1 3 ) .ident. P aus , ##EQU00058##
wherein y is a point on the second circle, and P.sub.aus is i the
distance value of the third distance; determining a fifth value as
equal to a value of a first point of intersection between the first
circle and the second circle; determining a sixth value as equal to
a value of a second point of intersection between the first circle
and the second circle that is different from the first point of
intersection; determining the first matching network using the
first source reflection factor, the fifth value of the transformed
first source reflection factor, the first load reflection factor,
and the third value of the transformed first load reflection
factor; and determining the second matching network using the
second source reflection factor, the sixth value of the transformed
second source reflection factor, the second load reflection factor,
and the fourth value of the transformed second load reflection
factor.
9. The method according to claim 8, wherein the circuit has a first
source element with a first source output and with a first source
reflection factor, wherein the circuit has a second source element
with a second source output and with a second source reflection
factor, wherein the circuit has a load, wherein the circuit has a
T-section with a first input, a second input, and an output,
wherein the T-section has a first load reflection factor into the
first input, wherein the T-section has a second load reflection
factor into the second input, wherein the output of the T-section
is connected to the load, wherein the circuit has a first matching
network with a first connection and a second connection, wherein
the second connection is connected to the first source output and
the first connection is connected to the first input of the
T-section, wherein a transformed first load reflection factor into
the second connection and a transformed first source reflection
factor into the first connection are achieved via the first
matching network, wherein the circuit has a second matching network
with a third connection and a fourth connection, wherein the fourth
connection is connectable to the second source output and the third
connection is connectable to the second input of the T-section,
wherein a transformed second load reflection factor into the fourth
connection and a transformed second source reflection factor into
the third connection are achieved via the second matching network,
wherein a first value of the transformed first load reflection
factor is determined, wherein the first source element has a first
optimum of a first parameter for the first value of the transformed
first load reflection factor acting at the first source output,
wherein the first value of the transformed first load reflection
factor differs from the complex conjugate of the first source
reflection factor, wherein a second value of the transformed second
load reflection factor is determined, wherein the second source
element has a second optimum of a second parameter for the second
value of the transformed second load reflection factor acting at
the second source output, and wherein the second value of the
transformed second load reflection factor differs from the complex
conjugate of the second source reflection factor.
10. The method according to claim 8, wherein P.sub.1 is the first
distance, a' is a transformed first load reflection factor, a'* is
a complex conjugate of the transformed first load reflection
factor, and a'.sub.opt is the first value.
11. The method according to claim 8, wherein P.sub.2 is the second
distance, c' is the transformed second load reflection factor, c'*
is the complex conjugate of the transformed second load reflection
factor and c'.sub.opt is the second value.
12. The method according to claim 8, wherein P.sub.3 is the third
distance, b is the first source reflection factor, b* is the
complex conjugate of the first source reflection factor, and a' is
the transformed first load reflection factor.
13. The method according to claim 8, wherein P.sub.4 is the fourth
distance, d is the second source reflection factor, d* is the
complex conjugate of the second source reflection factor, and c' is
the transformed second load reflection factor.
14. The method according to claim 8, wherein the distance value,
the third value, and the fourth value are defined in that: a
minimum of the geometric mean of the first distance and the second
distance is determined under the boundary condition that the third
distance is equal to the fourth distance and is not zero, the
transformed first load reflection factor and the transformed second
load reflection factor are varied, the complex conjugate of the
first source reflection factor, the complex conjugate of the second
source reflection factor, the first value, and the second value
have fixed values, and the value of the third distance associated
with the minimum is set as the distance value, the value of the
transformed first load reflection factor associated with the
minimum is set as the third value, and the value of the transformed
second load reflection factor associated with the minimum is set as
the fourth value,
15. An electronic circuit comprising: at least one source element;
at least one load; and at least one matching network that is
designed according to the method of claim 1.
16. The electronic circuit comprising: a first source element; a
second source element; a first matching network; and a second
matching network, wherein the first matching network and the second
matching network are designed according to the method of claim 7,
wherein the second source element is configured to output a signal
with a center frequency, wherein the load has a load impedance,
wherein the second matching network has line-like series elements
that carry the signal, wherein the line-like series elements only
have line impedances less than the load impedance, or wherein a sum
of the electrical lengths of the line-like series elements, each of
which has a line impedance greater than the load impedance, is less
than one quarter of a wavelength associated with the signal.
Description
[0001] This nonprovisional application is a continuation of
International Application No. PCT/EP2011/002074, which was filed on
Apr. 24, 2011, and which claims priority to German Patent
Application No. DE 10 2010 018 274.5, which was filed in Germany on
Apr. 25, 2010, and which are both herein incorporated by
reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention concerns a method for designing an
electronic circuit with a matching network.
[0004] 2. Description of the Background Art
[0005] The fundamentals of conformal mapping of circular regions
are known from "Uber eine Eigenschaft der konformen Abbildung
kreisformiger Bereiche" (On a property of conformal mapping of
circular regions), Georg Pick, Mathematische Annalen, Vol. 77,
1916, pages 1-6. The Poincare disk model is known from sources such
as, e.g., "Hyperbolische Geometrie" (Hyperbolic geometry), T.
Peters, pages 6 and 7, Sep. 3, 2003. The Poincare distance is known
from "Invariant Distances and Metrics in Complex
Analysis--revisited," M. Jarnicki, P. Pflug, page 7, February 2004.
In addition, the Mobius transformation is known from the lecture
notes "Komplexe Analysis," Prof. Dr. Dirk Ferus, 2008, pages 18 to
26. The Mobius transformation is used in Smith charts for
high-frequency engineering, for instance. The operation of matching
networks in circuits in high-frequency engineering can be
represented graphically using the Smith chart.
[0006] Matching networks can be used in a Doherty power amplifier,
for example. A Doherty power amplifier is known from, e.g., "The
Doherty Power Amplifier," Bumman K. et al, IEEE Microwave Magazine,
pages 42-50, October 2006, or "Practical Magic," R. Sweeney, IEEE
Microwave Magazine, pages 73-82, April 2008, or "Power Amplifiers
and Transmitters for RF and Microwave," F. H. Raab et al, IEEE
Transactions on Microwave Theory and Techniques, Vol. 50, No. 3,
pages 814-826, March 2002, or "A New High Efficiency Power
Amplifier for Modulated Waves," W. H. Doherty, Proceedings of the
Institute of Radio Engineers, Vol. 24, No. 9, pages 1163-1182,
September 1936.
SUMMARY OF THE INVENTION
[0007] It is an object of the invention to improve a method for
designing an electronic circuit to the greatest extent
possible.
[0008] According to an embodiment, a method is provided for
designing an electronic circuit to optimize a first parameter of
the circuit. The first parameter of the circuit is, for example, an
S-parameter, or a small-signal noise figure, or an effective input
reflection factor, or an effective output reflection factor, or an
effective output resistance, or a Rollett stability factor, or a
power gain, or an nth order intermodulation product, or an nth
order harmonic distortion, or a distortion factor, or an efficiency
of the power gain, or a noise figure, or a compression point, or a
compression gain, or a compression of the power gain, or an average
of a small-signal parameter, or an integral of a small-signal
parameter.
[0009] The circuit has a first matching network with a first
connection and a second connection. The circuit has a load
connected to the first connection. A first load reflection factor
that depends on the load is achieved at the first connection of the
first matching network. A first source element is connected to the
second connection of the first matching network, wherein the first
source element has a first source reflection factor. The first
source element is, for example, an amplifier or a signal line. The
load is, for example, an amplifier input or an antenna. The first
load reflection factor and the first source reflection factor are
determined by measurement or starting from a measurement,
preferably in an automated fashion.
[0010] In circuit design, it becomes necessary to tune to one
another the impedance levels of subsections or components that
follow one another in the signal path.
[0011] This is a function of separate, interposed functional
blocks, called matching networks. As a matching structure, the
matching network can have an L structure and/or a T structure
and/or a pi structure, for example.
[0012] A transformed first load reflection factor into the second
connection of the first matching network, and a transformed first
source reflection factor into the first connection of the first
matching network are achieved by means of the first matching
network. Preferably, the first matching network is reciprocal and
lossless.
[0013] The method for designing the electronic circuit can be
carried out fully automatically--in particular, under computer
control. To this end, measurement data of elements of the circuit,
such as transistors, impedances, and the like, are determined by
measurements. The measurement data are entered in a program
execution for calculating the elements of the matching network of
the electronic circuit. By this means, it is possible to calculate
the, e.g. capacitive or inductive, elements of the matching
network. Human intervention in the method is not necessary,
however.
[0014] The method for designing the circuit has multiple steps. In
a first step, a first value of the transformed first source
reflection factor and a second value of the transformed first load
reflection factor are determined. Multiple subsidiary steps are
provided for the determination of the first value and second value.
A number of first distances are determined. In this context, the
first distances are not Euclidean distances, but instead are what
are known as Poincare distances.
[0015] For each first distance from among the number of first
distances, a first circle is determined as the set of all points at
a first distance from the complex conjugate of the first load
reflection factor. The first circle is defined by
P ( y , a on * ) = arctanh ( y - a on * 1 - y * a on * ) .ident. P
R ( 1 ) ##EQU00001##
[0016] Here, P(y,a.sub.on*) is the Poincare distance, y is a point
on the first circle, y* is the complex conjugate of a point on the
first circle, a* is the complex conjugate of the first load
reflection factor, and P.sub.R is the first distance.
[0017] For each first distance from among the number of first
distances, a second circle is determined as the set of all points
at a first distance from the complex conjugate of the first source
reflection factor. The second circle is defined by
P ( x , b on * ) = arctanh ( x - b on * 1 - x * b on * ) .ident. P
R ( 2 ) ##EQU00002##
[0018] Here, P(y,b.sub.on*) is the Poincare distance, x is a point
on the second circle, x* is the complex conjugate of a point on the
second circle, b* is the complex conjugate of the first source
reflection factor, and P.sub.R is the first distance.
[0019] In the method, an arbitrary or predefinable number of first
point pairs is determined. A first pair point of each point pair is
on the first circle. A second pair point of each point pair is on
the second circle.
[0020] A value for the first parameter is determined for each first
point pair. The first pair point is equal to a value of the
transformed first source reflection factor. A second pair point is
equal to a value of the transformed first load reflection
factor.
[0021] An optimum of the first parameter is determined from all
values of the first parameter that are associated with the first
point pairs. A first value pair is determined from the first point
pairs, wherein the optimum of the parameter is associated with the
first value pair. The optimum is a local or global minimum or
maximum of the parameter. It is advantageous to determine a
suboptimum for each circle in an intermediate step. The optimum for
all circles can subsequently be determined from the suboptima.
[0022] A first value of the transformed first source reflection
factor equal to a first value point of the first value pair is
determined. A second value of the transformed first load reflection
factor equal to a second value point of the first value pair is
determined. The determination can take place by means of
calculation using models and/or measurements of the parameters of
the circuit, for example.
[0023] In a subsequent step of the method, a determination of the
first matching network takes place using the first value of the
transformed first source reflection factor, the second value of the
transformed first load reflection factor, the first source
reflection factor, and the first load reflection factor. The step
of determining the first matching network can likewise be performed
in an automated fashion. For example, a topology, which is to say
the arrangement of the capacitances and inductances of the first
matching network, is selected. Subsequently, the capacitance values
and the inductance values of the first matching network are
calculated from the first value of the transformed first source
reflection factor, the second value of the transformed first load
reflection factor, the first source reflection factor, and the
first load reflection factor.
[0024] The refinements described below also relate to the method
described above.
[0025] According to an especially advantageous refinement, the
method has additional steps. In this context, a first function is
defined that describes the transforming action of the first
matching network in the forward direction. The forward direction
here is defined as proceeding from the source element toward the
load. The first function is defined by
f a on , a on ' , .PHI. ( z 1 ) = .PHI. z 1 - z 0 1 - z 0 * z 1 ( 3
) with z 0 = 1 - a on 2 a on 2 a on ' 2 - 1 a on ' - .PHI. - 1 - a
on ' 2 a on 2 a on ' 2 - 1 a on ( 4 ) ##EQU00003##
[0026] In the first function, a.sub.on is the first load reflection
factor, a.sub.on' is the transformed first load reflection factor,
and .phi..epsilon.[0 . . . 2.pi.[ is a parameter. The imaginary
number i is defined by i=2 {square root over (-1)}, and z.sub.1 is
a first argument of the first function.
[0027] In addition, a second function is determined that describes
the transforming action of the first matching network in the
reverse direction. In this context, the reverse direction is
defined as proceeding from the load toward the source element. The
second function is defined by
f a on , a on ' , .PHI. R ( z 2 ) = .PHI. z 2 - z 0 R 1 - z 0 R * z
2 ( 5 ) with z 0 R = 1 - a on ' * 2 a on ' * 2 a on * 2 - 1 a on *
- .PHI. - 1 - a on * 2 a on ' * 2 a on * 2 - 1 a on ' * ( 6 )
##EQU00004##
[0028] Here, a.sub.on is the first load reflection factor,
a.sub.on* is the complex conjugate of the first load reflection
factor, a.sub.on' is the transformed first load reflection factor,
a.sub.on'* is the complex conjugate of the transformed first load
reflection factor, .phi..epsilon.[0 . . . 2.pi.[ is once again the
parameter already mentioned above, and z.sub.2 is a second argument
of the second function.
[0029] According to an embodiment of the method, the
above-described method has additional steps. Here, a value of the
parameter .phi..epsilon.[0 . . . 2[ is determined for the optimum
of the first parameter. The optimum is, for example, a minimum of
the first parameter, when the first parameter is, e.g., a
distortion factor. The optimum can also be a maximum of the first
parameter--such as a power gain, for example.
[0030] To determine the value of the parameter, the number of first
distances is equal to one. The first distance is determined between
the transformed first load reflection factor and the complex
conjugate of the first source reflection factor. In this
refinement, the transformed first load reflection factor is
predetermined or fixed.
[0031] The first distance here is defined as the Poincare distance
by
P a on ' , b on * = arctanh ( a on ' - b on * 1 - b on a on ' )
.ident. P R ( 7 ) ##EQU00005##
[0032] Here, b.sub.on is the first source reflection factor,
b.sub.on* is the complex conjugate of the first source reflection
factor, a.sub.on' is the transformed first load reflection factor,
and P.sub.R is the first distance.
[0033] The value of the parameter is determined, wherein, for the
value of the parameter, the second function with the first source
reflection factor as its second argument assumes the first value of
the transformed first source reflection factor as the function
value.
[0034] The first value of the transformed first source reflection
factor is determined as a point on the first circle, wherein the
first parameter is an optimum at the point. To this end, for
example, the parameter is determined for each of a number of points
on the first circle. For example, the point associated with the
maximal parameter is determined as the transformed first source
reflection factor.
[0035] Thereafter, the value of the parameter is determined. For
the value of the parameter, the second function with the first
source reflection factor as its second argument assumes the first
value determined of the transformed first source reflection factor
as the function value. In this case, the following applies:
f.sup.Ra.sub.on,a.sub.on',.phi..sub.opt(b.sub.on)=b.sub.on'.sub.opt
(8)
[0036] Subsequently, the first matching network is determined using
the first function for the value of the parameter. Here, the
particular transforming action is sought that uniquely describes
the matching network that maps the first load reflection factor
onto the transformed first load reflection factor and maps the
first source reflection factor onto the transformed first source
reflection factor. In this context, the transformed first load
reflection factor and the transformed first source reflection
factor may be identical to the first value determined or the second
value determined, respectively.
[0037] In an embodiment, the first parameter is the mismatch
between the first transformed source reflection factor and the
first load reflection factor.
[0038] According to another embodiment, a predetermined mismatch
between the first transformed source reflection factor and the
first load reflection factor is a part of the first parameter as
boundary condition.
[0039] Accordingly, a method is provided for designing an
electronic circuit to optimize a second parameter of the circuit.
The second parameter can match the first parameter or can be
different therefrom. The second parameter is, for example, an
S-parameter, or a small-signal noise figure, or an effective input
reflection factor, or an effective output reflection factor, or an
effective output resistance, or a Rollett stability factor, or a
power gain, or an nth order intermodulation product, or an nth
order harmonic distortion, or a distortion factor, or an efficiency
of the power gain, or a noise figure, or a compression point, or a
compression gain, or a compression of the power gain, or an average
of a small-signal parameter, or an integral of a small-signal
parameter.
[0040] The terms second, third, etc., used hereinafter have the
sole purpose of better clarity, and do not presuppose a first
connection, first element, etc.
[0041] The circuit has a second matching network with a third
connection and a fourth connection.
[0042] The circuit has, connected to the third connection, a
variable load with a first operating state and a second operating
state. The variable load has a third load reflection factor in the
first operating state and a second load reflection factor in the
second operating state.
[0043] The circuit preferably has a second source element with a
second source reflection factor connected to the fourth
connection.
[0044] By means of the second matching network, a transformed third
load reflection factor into the fourth connection is achieved in
the first operating state, and a transformed second load reflection
factor is achieved in the second operating state. Preferably, the
transformed second source reflection factor into the third
connection is achieved by means of the second matching network.
[0045] For example, the transformed second load reflection factor,
and the transformed third load reflection factor, and the second
load reflection factor are predetermined by requirements from the
circuit--for example, matching the second source reflection
factor.
[0046] The method has multiple steps. In the method, a third value
of the third load reflection factor and a fourth value of the
second load reflection factor are determined. To this end, a third
distance between the transformed second load reflection factor and
the transformed third load reflection factor is determined first.
The third distance is defined by
P 3 = arctanh ( c off ' - c on ' 1 - c off ' * c on ' ) ( 9 )
##EQU00006##
[0047] Here, c.sub.on' is the transformed second load reflection
factor, c.sub.off' is the transformed third load reflection factor,
c.sub.on'* is the complex conjugate of the transformed second load
reflection factor, and P.sub.3 is the third distance.
[0048] Thereafter, a third circle is determined as the set of all
points at the third distance from the second load reflection
factor. The third circle is defined by
P ( z , c on ) = arctanh ( z - c on 1 - z * c on ) .ident. P 3 ( 10
) ##EQU00007##
[0049] Here, P(z, c.sub.on) is the Poincare distance, z is a point
on the third circle, z* is the complex conjugate of the point on
the third circle, c.sub.on is the second load reflection factor,
c.sub.on* is the complex conjugate of the second load reflection
factor, and P.sub.3 is the third distance.
[0050] In the method, a number of second point pairs is determined.
A second pair point of each point pair is a point on the third
circle.
[0051] A value for the second parameter is determined for each
second point pair. A value of the third load reflection factor is
equal to the second pair point. A value of the second load
reflection factor is equal to the first pair point. For the
determination, the value of the second parameter is calculated, for
example.
[0052] In the method, an optimum of the second parameter is
determined from all values of the second parameter. In so doing,
the values of the second parameter are associated with the point
pairs. The optimum is a local or global minimum or maximum of the
parameter.
[0053] Thereafter, a second point pair associated with the optimum
is determined. The third value of the third load reflection factor
is determined as equal to a second pair point, associated with the
optimum, of the second point pair associated with the optimum. The
fourth value of the second load reflection factor is determined as
equal to a first pair point, associated with the optimum, of the
second point pair associated with the optimum.
[0054] In a subsequent step of the method, a determination of the
second matching network takes place using the third value of the
third load reflection factor, the fourth value of the second load
reflection factor, the transformed second load reflection factor,
and the transformed third load reflection factor. The step of
determining the second matching network can likewise be performed
in an automated fashion. For example, a topology, which is to say
the arrangement of the capacitances and inductances of the second
matching network, is selected. Subsequently, the capacitance values
and the inductance values of the second matching network are
calculated from the third value of the third load reflection
factor, the fourth value of the second load reflection factor, the
transformed second load reflection factor, and the transformed
third load reflection factor.
[0055] Accordingly, a method is provided for designing an
electronic circuit. The circuit has a first operating state and a
second operating state. The circuit has a first source element with
a first source output and a second source element with a second
source output. Preferably, the first source element is a first
amplifier and the second source element is a second amplifier.
Preferably, the first amplifier and the second amplifier are
components of a Doherty amplifier. The first amplifier and/or the
second amplifier preferably have an LDMOS transistor for gain.
[0056] In the first operating state, the first source element has a
first source reflection factor into the first source output.
[0057] The circuit has a load with a load input. The load has a
load input reflection factor into the load input. Accordingly, the
load has a load impedance.
[0058] The circuit has a T-section with a first input, a second
input, and an output. The load input of the load is connected to
the output of the T-section. The T-section is preferably a T-shaped
conductor that preferably is made of metal. The T-section is
integrated on a semiconductor chip, for example.
[0059] The T-section has a first load reflection factor into the
first input in the second operating state. The T-section has a
second load reflection factor into the second input in the first
operating state. The T-section has a third load reflection factor
into the second input in the second operating state.
[0060] The circuit has a first matching network with a first
connection and a second connection. The first connection is
connected to the first input of the T-section. The second
connection is connected to the first source output of the first
source element.
[0061] In the first operating state, the first matching network has
a transformed first source reflection factor into the first
connection. In the second operating state, the first matching
network has a transformed first load reflection factor into the
second connection.
[0062] The circuit has a second matching network with a third
connection and a fourth connection. The third connection is
connected to the second input of the T-section.
[0063] The fourth connection of the second matching network is
connected to the second source output.
[0064] In the first operating state, the second matching network
has a transformed second load reflection factor into the fourth
connection. In the second operating state, the second matching
network has a transformed third load reflection factor into the
fourth connection.
[0065] A first value of the transformed first load reflection
factor is determined for optimizing a parameter of the circuit in
that a measurement is carried out in the second operating state. A
second value of the transformed second load reflection factor is
determined for optimizing the parameter of the circuit in that a
measurement is carried out in the first operating state. A third
value of the transformed third load reflection factor is determined
for optimizing the parameter of the circuit in that a measurement
is carried out in the second operating state.
[0066] In the method, the first load reflection factor is set to a
first initial value. The first initial value can be set arbitrarily
or using the load input reflection factor, for example. Likewise,
the second load reflection factor is set to a second initial value.
The second initial value can be set arbitrarily or using the load
input reflection factor, for example.
[0067] The method has multiple steps. In one step, a first distance
between the first value and the complex conjugate of the first
source reflection factor is determined by
P 1 = arctanh ( a on opt ' - b off * 1 - b off * a on opt ' * ) (
11 ) ##EQU00008##
[0068] Here, b.sub.off is the first source reflection factor,
b.sub.off* is the complex conjugate of the first source reflection
factor, a.sub.on'.sub.opt is the first value of the transformed
first load reflection factor, and P.sub.1 is the first
distance.
[0069] In another step, a first circle is determined as the set of
all points at the calculated first distance from the complex
conjugate of the first load reflection factor by
P ( y , a on * ) = arctanh ( y - a on * 1 - y * a on * ) .ident. P
1 ( 12 ) ##EQU00009##
[0070] Here, y is a point on the first circle, y* is the complex
conjugate of the point on the first circle, a.sub.on* is the
complex conjugate of the first load reflection factor, and P.sub.1
is the first distance.
[0071] In another step, a third distance between the second value
and the third value is determined by
P 3 = arctanh ( c on opt ' - c off opt ' 1 - c on opt ' * c off opt
' ) ( 13 ) ##EQU00010##
[0072] Here, c.sub.off'.sub.opt is the second value of the
transformed second load reflection factor, c.sub.on'.sub.opt is the
third value of the transformed third load reflection factor, and
c.sub.on'.sub.opt* is the complex conjugate of the third value of
the transformed third load reflection factor.
[0073] In another step, a third circle is determined as the set of
all points at the third distance from the third load reflection
factor by
P ( z , c on ) = arctanh ( z - c on 1 - z * c on ) .ident. P 3 ( 14
) ##EQU00011##
[0074] Here, z is a point on the third circle, z* is the complex
conjugate of the point on the third circle, c.sub.on is the third
load reflection factor, c.sub.on* is the complex conjugate of the
third load reflection factor, and P.sub.3 is the third
distance.
[0075] In the method, a modified first circle is determined. This
modified first circle can also be called an image circle. In this
context, the modified first circle is determined as the set of all
modified reflection factors, wherein an overall impedance is
associated with each of the modified reflection factors. Each
overall impedance is determined from a first parallel circuit of a
load impedance of the load and an impedance associated with a
reflection factor on the first circle. Here, the load impedance is
associated with the load input reflection factor of the load.
[0076] In the method, at least one fourth value of the second load
reflection factor is determined, wherein a sum of squares of the
distances between the fourth value and the third circle and between
the fourth value and the modified first circle is minimized for the
at least one fourth value.
[0077] In the method, a fifth value of the transformed first source
reflection factor is determined for each fourth value of the second
load reflection factor. In this process a fourth impedance is
determined, wherein the fourth impedance is associated with the
fourth value of the second load reflection factor. A fifth
impedance is determined so that a second parallel circuit of the
fifth impedance with the load impedance is equal to the fourth
impedance, wherein the fifth value of the transformed first source
reflection factor is associated with the fifth impedance.
[0078] In the method, the first matching network is determined
using the first load reflection factor, the first value of the
transformed first load reflection factor, the first source
reflection factor, and the fifth value of the transformed first
source reflection factor.
[0079] In the method, the second matching network is determined
using the second value of the transformed second load reflection
factor, the third value of the transformed third load reflection
factor, the third load reflection factor, and the fourth value of
the second load reflection factor.
[0080] Accordingly, a method for designing an electronic circuit is
provided. The circuit has a first source element with a first
source output and with a first source reflection factor.
[0081] The circuit has a second source element with a second source
output and with a second source reflection factor. The circuit also
has a load. The load can be composed of one or more elements. The
circuit has a T-section with a first input, and a second input, and
an output.
[0082] The T-section has a first load reflection factor into the
first input. The T-section has a second load reflection factor into
the second input. The output of the T-section is connected to the
load.
[0083] The circuit has a first matching network with a first
connection and a second connection. The second connection of the
first matching network is connected to the first source output of
the first source element. The first connection of the first
matching network is connected to the first input of the
T-section.
[0084] By means of the first matching network, a transformed first
load reflection factor into the second connection and a transformed
first source reflection factor into the first connection are
achieved.
[0085] The circuit has a second matching network with a third
connection and a fourth connection. The fourth connection of the
second matching network is connected to the second source output of
the second source element. The third connection of the second
matching network is connected to the second input of the
T-section.
[0086] By means of the second matching network, a transformed
second load reflection factor into the fourth connection and a
transformed second source reflection factor into the third
connection are achieved.
[0087] A first value of the transformed first load reflection
factor is determined. The first source element has a first optimum
of a first parameter for the first value of the transformed first
load reflection factor acting at the first source output. Thus, if
the first source output is precisely terminated with the first
transformed load reflection factor, the first parameter is minimal
or maximal, for example. In accordance with a boundary condition,
the first value of the transformed first load reflection factor
differs from the complex conjugate of the first source reflection
factor.
[0088] A second value of the transformed second load reflection
factor is determined. The second source element has a second
optimum of a second parameter for the second value of the
transformed second load reflection factor acting at the second
source output. Here, the second value of the transformed second
load reflection factor differs from the complex conjugate of the
second source reflection factor. Preferably the first parameter and
the second parameter are equal.
[0089] Under the stated boundary conditions, the steps of the
method are a significant part of the invention. The method for
designing the electronic circuit is carried out fully
automatically--in particular, under computer control. To this end,
measurement data of elements of the circuit, such as transistors,
impedances, and the like, are determined by measurements. The
measurement data are entered in a program execution for calculating
the elements of the matching networks of the electronic circuit. By
this means, it is possible to calculate the, e.g. capacitive or
inductive, elements of the matching network. Human intervention in
the method is not necessary, however. The matching networks are
subsequently integrated onto a chip together with other circuit
components, for example.
[0090] The method for designing the electronic circuit has multiple
steps.
[0091] In one step, a distance value, and a third value of the
transformed first load reflection factor, and a fourth value of the
transformed second load reflection factor are determined. To this
end, a first distance between the first value and the transformed
first load reflection factor is defined by
P 1 = arctanh ( a opt ' - a ' 1 - a ' * a opt ' ) ( 15 )
##EQU00012##
[0092] Here, P.sub.1 is the first distance, a' is the transformed
first load reflection factor, a'* is the complex conjugate of the
transformed first load reflection factor, and a'.sub.opt is the
first value.
[0093] To this end, a second distance between the second value and
the transformed second load reflection factor is defined by:
P 2 = arctanh ( c opt ' - c ' 1 - c ' * c opt ' ) ( 16 )
##EQU00013##
[0094] Here, P.sub.2 is the second distance, c' is the transformed
second load reflection factor, c'* is the complex conjugate of the
transformed second load reflection factor, and c'.sub.opt is the
second value.
[0095] To this end, a third distance between the transformed first
load reflection factor and the complex conjugate of the first
source reflection factor is defined by:
P 3 = arctan h ( a ' - b * 1 - ba ' ) ( 17 ) ##EQU00014##
[0096] Here, P.sub.3 is the third distance, b is the first source
reflection factor, b* is the complex conjugate of the first source
reflection factor, and a' is the transformed first load reflection
factor.
[0097] To this end, a fourth distance between the transformed
second load reflection factor and the complex conjugate of the
second source reflection factor is defined by:
P 4 = arctan h ( c ' - d * 1 - dc ' ) ( 18 ) ##EQU00015##
[0098] Here, P.sub.4 is the fourth distance, d is the second source
reflection factor, d* is the complex conjugate of the second source
reflection factor, and c' is the transformed second load reflection
factor. The first distance, the second distance, the third
distance, and the fourth distance can also be referred to as
Poincare distances.
[0099] In another step, the distance value, and the third value,
and the fourth value are defined in that a minimum of the geometric
mean of the first distance and second distance is determined under
the boundary condition that the third distance is equal to the
fourth distance and is not zero. For determining the minimum, the
transformed first load reflection factor and the transformed second
load reflection factor are varied. In contrast therewith, the
complex conjugate of the first source reflection factor, the
complex conjugate of the second source reflection factor, the first
value, and the second value have fixed values.
[0100] Here, for example, for determining the minimum, the
following applies:
{square root over (P.sub.1.sup.2+P.sub.2.sup.2)}=min (19)
[0101] In addition, the value of the third distance associated with
the minimum is set as the distance value, and the value of the
transformed first load reflection factor associated with the
minimum is set as the third value, and the value of the transformed
second load reflection factor associated with the minimum is set as
the fourth value.
[0102] In another step, a fifth value of the transformed first
source reflection factor and a sixth value of the transformed
second source reflection factor are determined. To this end, a
first circle with a real center point is determined that intersects
a real reflection factor value of one third and a real reflection
factor value of minus one.
[0103] In addition, a second circle as the set of all points with a
distance from the real reflection factor value of one third equal
to the distance value is determined by:
P ( y , 1 3 ) = arctan h ( y - 1 3 1 - y 1 3 ) .ident. P aus ( 20 )
##EQU00016##
[0104] Here, y is a point on the second circle, and P.sub.aus is i
the distance value of the third distance.
[0105] In addition, the fifth value is determined as equal to a
first point of intersection between the first circle and the second
circle, and the sixth value is determined as equal to a second
point of intersection between the first circle and the second
circle different from the first point of intersection.
[0106] In another step, the first matching network is determined
using the first source reflection factor, and the transformed first
source reflection factor, and the third value of the transformed
first load reflection factor.
[0107] In another step, the second matching network is determined
using the second source reflection factor, and the transformed
second source reflection factor, and the fourth value of the
transformed second load reflection factor.
[0108] In one step, the first matching network is determined using
the first source reflection factor, and the fifth value (of the
transformed first source reflection factor, and the first load
reflection factor, and the third value of the transformed first
load reflection factor.
[0109] In one step, the second matching network is determined using
the second source reflection factor, and the sixth value of the
transformed second source reflection factor, and the second load
reflection factor, and the fourth value of the transformed second
load reflection factor.
[0110] The invention has the additional object of specifying a
circuit that has been improved to the greatest extent possible.
[0111] Accordingly, an electronic circuit with at least one source,
with at least one load, and with at least one matching network is
provided. The matching network is designed in accordance with one
of the methods explained above.
[0112] In an embodiment, the circuit has a first matching network
and a second matching network. The circuit has a first operating
state and a second operating state. The circuit has a first source
element with a first source output and a second source element with
a second source output. Preferably, the first source element is a
first amplifier, and the second source element is a second
amplifier. Preferably, the first amplifier and the second amplifier
are components of a Doherty amplifier. The first amplifier and/or
the second amplifier preferably has an LDMOS transistor for
gain.
[0113] In the first operating state, the first source element has a
first source reflection factor into the first source output.
[0114] The circuit has a load with a load input. The load has a
load input reflection factor into the load input. Accordingly, the
load has a load impedance.
[0115] The circuit has a T-section with a first input, a second
input, and an output. The load input of the load is connected to
the output of the T-section. The T-section is preferably a T-shaped
conductor that preferably is made of metal. The T-section is
integrated on a semiconductor chip, for example.
[0116] The T-section has a first load reflection factor into the
first input in the second operating state. The T-section has a
second load reflection factor into the second input in the first
operating state. The T-section has a third load reflection factor
into the second input in the second operating state.
[0117] The circuit has the first matching network with a first
connection and a second connection. The first connection is
connected to the first input of the T-section. The second
connection is connected to the first source output of the first
source element.
[0118] In the first operating state, the first matching network has
a transformed first source reflection factor into the first
connection. In the second operating state, the first matching
network has a transformed first load reflection factor into the
second connection.
[0119] The circuit has the second matching network with a third
connection and a fourth connection. The third connection is
connected to the second input of the T-section.
[0120] The fourth connection of the second matching network is
connected to the second source output.
[0121] In the first operating state, the second matching network
has a transformed second load reflection factor into the fourth
connection. In the second operating state, the second matching
network has a transformed third load reflection factor into the
fourth connection.
[0122] A first value of the transformed first load reflection
factor is determined for optimizing a parameter of the circuit in
that a measurement is carried out in the second operating state. A
second value of the transformed second load reflection factor is
determined for optimizing the parameter of the circuit in that a
measurement is carried out in the first operating state. A third
value of the transformed third load reflection factor is determined
for optimizing the parameter of the circuit in that a measurement
is carried out in the second operating state.
[0123] In this context, the matching networks are designed in that
the first load reflection factor is set to a first initial value.
The first initial value can be set arbitrarily or using the load
input reflection factor, for example. Likewise, the second load
reflection factor is set to a second initial value. The second
initial value can be set arbitrarily or using the load input
reflection factor, for example.
[0124] A first distance between the first value and the complex
conjugate of the first source reflection factor is determined
by:
P 1 = arctan h ( a on ' opt - b off * 1 - b off * a on ' opt * ) (
21 ) ##EQU00017##
[0125] Here, b.sub.off is the first source reflection factor,
b.sub.off* is the complex conjugate of the first source reflection
factor, a.sub.on'.sub.opt is the first value of the transformed
first load reflection factor, and P.sub.1 is the first
distance.
[0126] A first circle is determined as the set of all points at the
calculated first distance from the complex conjugate of the first
load reflection factor by:
P ( y , a on * ) = arctan h ( y - a on * 1 - y * a on * ) .ident. P
1 ( 22 ) ##EQU00018##
[0127] Here, y is a point on the first circle, y* is the complex
conjugate of the point on the first circle, a.sub.on* the complex
conjugate of the first load reflection factor, and P.sub.1 is the
first distance.
[0128] A third distance between the second value and the third
value is determined by:
P 3 = arctan h ( c on ' opt - c off ' opt 1 - c on ' opt * c off '
opt ) ( 23 ) ##EQU00019##
[0129] Here, c.sub.off'.sub.opt is the second value of the
transformed second load reflection factor, c.sub.on'.sub.opt is the
third value of the transformed third load reflection factor, and
c.sub.on'.sub.opt* is the conjugated complex of the third value of
the transformed third load reflection factor.
[0130] A third circle is determined as the set of all points at the
third distance from the third load reflection factor by:
P ( z , c on ) = arctan h ( z - c on 1 - z * c on ) .ident. P 3 (
24 ) ##EQU00020##
[0131] Here, z is a point on the third circle, z* is the complex
conjugate of the point on the third circle, c.sub.on is the third
load reflection factor, c.sub.on* is the complex conjugate of the
third load reflection factor, and P.sub.3 is the third
distance.
[0132] A modified first circle is determined. This modified first
circle can also be called an image circle. In this context, the
modified first circle is determined as the set of all modified
reflection factors, wherein an overall impedance is associated with
each of the modified reflection factors. Each overall impedance is
determined from a first parallel circuit of a load impedance of the
load and an impedance associated with a reflection factor on the
first circle. Here, the load impedance is associated with the load
input reflection factor of the load.
[0133] At least one fourth value of the second load reflection
factor is determined, wherein a sum of squares of the distances
between the fourth value and the third circle and between the
fourth value and the modified first circle is minimized for the at
least one fourth value.
[0134] A fifth value of the transformed first source reflection
factor is determined for each fourth value of the second load
reflection factor. In this process, a fourth impedance is
determined, wherein the fourth impedance is associated with the
fourth value of the second load reflection factor. A fifth
impedance is determined so that a second parallel circuit of the
fifth impedance with the load impedance is equal to the fourth
impedance, wherein the fifth value of the transformed first source
reflection factor is associated with the fifth impedance.
[0135] The first matching network is designed using the first load
reflection factor, the first value of the transformed first load
reflection factor, the first source reflection factor, and the
fifth value of the transformed first source reflection factor.
[0136] The second matching network is designed using the second
value of the transformed second load reflection factor, the third
value of the transformed third load reflection factor, the third
load reflection factor, and the fourth value of the second load
reflection factor.
[0137] The second source element is designed to output a signal
with a center frequency. The load has a load impedance. The second
matching network has line-like series elements that carry the
signal. The line-like series elements only have line impedances
less than the load impedance.
[0138] A sum of the electrical lengths of such line-like series
elements, each of which has a line impedance greater than the load
impedance, is less than one quarter of a conducted wavelength
associated with the signal.
[0139] The variant refinements described above are especially
advantageous, both singly and in combination. All variant
refinements may be combined with one another. Some possible
combinations are explained in the description of the exemplary
embodiments from the figures. The possible combinations of variant
refinements shown therein are not exhaustive, however.
[0140] Further scope of applicability of the present invention will
become apparent from the detailed description given hereinafter.
However, it should be understood that the detailed description and
specific examples, while indicating preferred embodiments of the
invention, are given by way of illustration only, since various
changes and modifications within the spirit and scope of the
invention will become apparent to those skilled in the art from
this detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0141] The present invention will become more fully understood from
the detailed description given hereinbelow and the accompanying
drawings which are given by way of illustration only, and thus, are
not limitive of the present invention, and wherein:
[0142] FIG. 1 is a series circuit arrangement such as is suitable
for high-frequency applications;
[0143] FIG. 2 is a schematic diagram with a first parameter;
[0144] FIG. 3 is a schematically represented Poincare circle;
[0145] FIG. 4 is another schematically represented Poincare
circle;
[0146] FIG. 5 is a schematic representation of load reflection
factors with regard to a matching network;
[0147] FIG. 6 is a Smith chart with Poincare circles;
[0148] FIG. 7 is a Smith chart with Poincare circles;
[0149] FIG. 8 is a Smith chart with two concentric families of
Poincare circles;
[0150] FIG. 9 is a circuit diagram with a variable load;
[0151] FIG. 10 is a schematic diagram with a second parameter;
[0152] FIG. 11 is another schematically represented Poincare
circle;
[0153] FIG. 12 is a schematic circuit diagram of a Doherty
load-modulation amplifier arrangement;
[0154] FIG. 13 is another schematic representation of two Poincare
circles;
[0155] FIG. 14 is another schematic representation of two Poincare
circles;
[0156] FIG. 15 is another Smith chart with Poincare circles;
[0157] FIG. 16 is another Smith chart with Poincare circles;
[0158] FIG. 17 to 19 are schematic equivalent circuits for signal
addition;
[0159] FIG. 20 is a schematic equivalent circuit with a
T-section;
[0160] FIG. 21 is a schematic equivalent circuit with
circulators;
[0161] FIG. 22 is a schematic circuit diagram of an amplifier
arrangement;
[0162] FIG. 23 is another schematic representation of two Poincare
circles;
[0163] FIG. 24 is a schematic diagram with a first parameter;
[0164] FIG. 25 is a schematic diagram with a second parameter;
[0165] FIG. 26 is a schematic representation of two Poincare
circles;
[0166] FIG. 27 is a schematic representation of an amplifier
arrangement;
[0167] FIG. 28 to 31 illustrate structure of a matching network;
and
[0168] FIG. 32 is a diagram of implemented structures of matching
networks.
DETAILED DESCRIPTION
[0169] In FIG. 1, a circuit is schematically represented as a block
diagram. The circuit has a first matching network M.sub.1 with a
first connection A.sub.1 and a second connection A.sub.2. The
circuit has a load L connected to the first connection A.sub.1.
[0170] A first load reflection factor a.sub.on that depends on the
load L is achieved at the first connection A.sub.1 of the first
matching network M.sub.1.
[0171] The circuit has, connected to the second connection A.sub.2
of the first matching network M.sub.1, a first source element
Q.sub.1 with a first source reflection factor b.sub.on. In the
exemplary embodiment in FIG. 1, a source output QA.sub.1 of the
first source element Q.sub.1 is connected to the second connection
A.sub.2 of the first matching network M.sub.1.
[0172] By means of the first matching network M.sub.1, a
transformed first load reflection factor a.sub.on' into the second
connection A.sub.2 and a transformed first source reflection factor
b.sub.on' into the first connection A.sub.1 are achieved.
[0173] FIG. 2 shows a diagram with a first parameter G1 of the
circuit from FIG. 1. In the method explained below, the electronic
circuit is designed to optimize the first parameter Cl. The first
parameter G1 in the exemplary embodiment in FIG. 2 depends on the
point pair [y(P.sub.R), y(P.sub.R)] and has a maximum Max.sub.1 for
the values [y.sub.opt, x.sub.opt] or [b.sub.on'.sub.opt,
a.sub.on'.sub.opt] as an optimum. A first value b.sub.on'.sub.opt
of the transformed first source reflection factor b.sub.on' and a
second value a.sub.on'.sub.opt of the transformed first load
reflection factor a.sub.on' are determined first.
[0174] In FIG. 3, a first circle K.sub.1 is shown schematically as
the set of all points at the first distance P.sub.R from the
complex conjugate a.sub.on* of the first load reflection factor
a.sub.on. The first circle is determined by:
P ( y , a on * ) = arctan h ( y - a on * 1 - y * a on * ) .ident. P
R ( 25 ) ##EQU00021##
[0175] Here, y is a point on the first circle K.sub.1, y* is the
complex conjugate of the point y on the first circle K.sub.1,
a.sub.on* is the complex conjugate a.sub.on* of the first load
reflection factor a.sub.on, and P.sub.R is the first distance
P.sub.R. The first circle K.sub.1 is determined here for each first
distance P.sub.R among a number of first distances P.sub.R.
[0176] In FIG. 4, a second circle K.sub.2 is shown schematically as
the set of all points at the first distance P.sub.R from the
complex conjugate b.sub.on* of the first source reflection factor
b.sub.on. The second circle K.sub.2 is determined by:
P ( x , b on * ) = arctan h ( x - b on * 1 - x * b on * ) .ident. P
R ( 26 ) ##EQU00022##
[0177] Here, x is a point on the second circle K.sub.2, x* is the
complex conjugate of the point x on the second circle K.sub.2,
b.sub.on* is the complex conjugate b.sub.on* of the first source
reflection factor b.sub.on, and P.sub.R is the first distance
P.sub.R. The second circle K.sub.2 is determined here for each
first distance P.sub.R among a number of first distances
P.sub.R.
[0178] In the method, a number of first point pairs [y(P.sub.R),
x(P.sub.R)] are determined. Here, as is shown in FIG. 3, a first
pair point y(P.sub.R) of each point pair [y(P.sub.R), x(P.sub.R)]
is on the first circle K.sub.1. As is shown in FIG. 4, a second
pair point x(P.sub.R) of each point pair [y(P.sub.R), x(P.sub.R)]
is on the second circle K.sub.2.
[0179] In the method, a value for the first parameter G1 is
determined for every first point pair [y(P.sub.R), x(P.sub.R)] with
the first pair point y(P.sub.R) equal to a value of the transformed
first source reflection factor b.sub.on' and with the second pair
point x(P.sub.R) equal to a value of the transformed first load
reflection factor a.sub.on'.
[0180] The optimum Max.sub.1 of the first parameter G.sub.1 is
determined from all values of the first parameter G.sub.1, that are
associated with the first point pairs [y(P.sub.R), x(P.sub.R)]. In
this process, a first value pair [y.sub.opt, x.sub.opt] is
determined from the first point pairs [y(P.sub.R), x(P.sub.R)],
wherein the optimum Max.sub.1 is associated with the first value
pair [y.sub.opt, x.sub.opt].
[0181] The first value b.sub.on'.sub.opt of the transformed first
source reflection factor b.sub.on' is equal to a first value point
y.sub.opt of the first value pair [y.sub.opt, x.sub.opt]. The
second value a.sub.on'.sub.opt of the transformed first load
reflection factor a.sub.on' is equal to a second value point
x.sub.opt of the first value pair [y.sub.opt, x.sub.opt].
[0182] The first matching network M.sub.1 in FIG. 1 is determined
using the first value b.sub.on'.sub.opt of the transformed first
source reflection factor b.sub.on', and the second value
a.sub.on'.sub.opt of the transformed first load reflection factor
a.sub.on', and the first source reflection factor b.sub.on, and the
first load reflection factor a.sub.on.
[0183] FIG. 1 shows the electronic circuit 1 by way of example as
an amplifier chain having a first amplifier as the first source
element Q.sub.1 with the source reflection factor b1, the matching
network M1 with the first connection A1 and the second connection
A2, and a load element L with the load reflection factor a1. The
load element L is, e.g., a second amplifier that is connected at
the input side to the first matching network M1. The first
connection A1 is connected to the load element L, and the second
connection A2 is connected to the source element Q1.
[0184] When an electrical signal, considered as, for example, a
voltage wave, passes through a discontinuity in the impedance of
the signal-carrying channel, Kirchhoff's laws require that a part
of the forward-traveling wave is reflected back. If the source
element Q1 operates with an output impedance into the load L with
an input impedance, the source element Q1 sees neither the load L
nor the input impedance, but only the reflected part of the signal
returning to the source element Q1.
[0185] Consequently, the quantity of primary importance for
high-frequency behavior is not so much the actual impedance as the
relevant reflection factor. Accordingly, in the exemplary
embodiments impedances and reflection factors are used, which can
be converted into one another through one-to-one mapping.
[0186] FIG. 9 shows a circuit that is to be designed for
high-frequency signals, for example. The circuit has a second
matching network M.sub.2 with a third connection A.sub.3 and a
fourth connection A.sub.4. The circuit has a variable load L with a
first operating state off and a second operating state on,
connected to the third connection A.sub.3. At the third connection
A.sub.3, a second load reflection factor c.sub.on is achieved in
the second operating state on, and a third load reflection factor
c.sub.off is achieved in the first operating state off. By means of
the second matching network M.sub.2, a transformed second load
reflection factor c.sub.on' into the fourth connection A.sub.4 is
achieved in the second operating state, and a transformed third
load reflection factor c.sub.off' is achieved in the first
operating state.
[0187] FIG. 10 shows a schematic diagram of a second parameter
G.sub.2 of the circuit from FIG. 9. In a method for designing the
electronic circuit from FIG. 9, the second parameter G.sub.2 of the
circuit is to be optimized. For example, the optimum, as shown in
FIG. 10, is a maximum Max.sub.2 of the second parameter
G.sub.2.
[0188] In FIG. 11, a third circle K3 about a second load reflection
factor c.sub.on is shown schematically. In a method for designing
the electronic circuit from FIG. 9, a third value c.sub.off,opt of
the third load reflection factor c.sub.off and a fourth value
c.sub.on,opt of the second load reflection factor c.sub.on are
determined.
[0189] To this end, a third distance P.sub.3 between the
transformed second load reflection factor c.sub.on' and the
transformed third load reflection factor c.sub.off' is determined
by:
P 3 = arctan h ( c off ' - c on ' 1 - c off ' * c on ' ) ( 27 )
##EQU00023##
[0190] Here, c.sub.on' is the transformed second load reflection
factor c.sub.on', c.sub.off' is the transformed third load
reflection factor c.sub.off', c.sub.off'* is the complex conjugate
c.sub.off'* of the transformed third load reflection factor
c.sub.off', and P.sub.3 is the third distance P.sub.3.
[0191] In FIG. 11, a third circle K.sub.3 is shown schematically.
The third circle K.sub.3 is determined as the set of all points at
the third distance P.sub.3 from the second load reflection factor
c.sub.on by:
P ( z , c on ) = arctan h ( z - c on 1 - z * c on ) .ident. P 3 (
28 ) ##EQU00024##
[0192] Here, z is a point on the third circle K.sub.3, z* is the
complex conjugate z* of the point z on the third circle K.sub.3,
c.sub.on is the second load reflection factor c.sub.on, c.sub.on*
is the complex conjugate c.sub.on* of the second load reflection
factor c.sub.on, and P.sub.3 is the third distance P.sub.3.
[0193] A number of second point pairs [c.sub.on, z(P.sub.3)] are
determined. Here, a second pair point z(P.sub.3) of each second
point pair [c.sub.on, z(P.sub.3)] is a point on the third circle
K.sub.3, which is shown schematically in FIG. 11. In accordance
with FIG. 10, a value of the second parameter G.sub.2 is determined
for every second point pair [c.sub.on, z(P.sub.3)]. In FIG. 10, the
behavior of the second parameter G2 is shown schematically as a
function of the second point pairs [c.sub.on, z(P.sub.3)]. A value
of the third load reflection factor c.sub.off here is equal to the
second pair point z(P.sub.3). A value of the second load reflection
factor c.sub.on is equal to the first pair point c.sub.on.
[0194] The optimum Max.sub.2 of the second parameter G.sub.2 shown
in FIG. 10 is determined from all values of the second parameter
G.sub.2 that are associated with the second point pairs [c.sub.on,
z(P.sub.3)].
[0195] In accordance with FIG. 10, a second point pair
[c.sub.on,opt, c.sub.off,opt] is determined that is associated with
the optimum Max.sub.2. The third value c.sub.off,opt of the third
load reflection factor c.sub.off is determined as equal to a second
pair point c.sub.off,opt associated with the optimum Max.sub.2, of
the second point pair [c.sub.on,opt, c.sub.off,opt] associated with
the optimum Max.sub.2. The fourth value c.sub.on,opt of the second
load reflection factor c.sub.on is determined as equal to a first
pair point c.sub.on, associated with the optimum Max.sub.2, of the
second point pair [c.sub.on,opt, c.sub.off,opt] associated with the
optimum Max.sub.2.
[0196] The second matching network M.sub.2 in the exemplary
embodiment in FIG. 9 is determined using the third value
c.sub.off,opt of the third load reflection factor c.sub.off, and
the fourth value c.sub.on,opt of the second load reflection factor
c.sub.on, and the transformed second load reflection factor
c.sub.on', and the transformed third load reflection factor
c.sub.off'.
[0197] FIG. 12 shows an electronic circuit of an exemplary
embodiment that is to be designed. The circuit has a first
operating state off and a second operating state on. In FIG. 12,
the reflection factors are labeled in accordance with the
associated operating state.
[0198] The circuit has a first source element Q.sub.1 with a first
source output QA.sub.1, and a second source element Q.sub.2 with a
second source output QA.sub.2. In the first operating state off,
the first source element Q.sub.1 has a first source reflection
factor b.sub.off into the first source output QA.sub.1.
[0199] The circuit has a load L with a load input LE. The load L
has a load input reflection factor r into the load input LE.
[0200] The circuit [has] a T-section T with a first input E.sub.1,
and a second input E.sub.2, and an output E.sub.3. The load input
LE of the load L is connected to the output E.sub.3 of the
T-section T. The T-section T has a first load reflection factor
a.sub.on into the first input E.sub.1 in the second operating state
on. The T-section T has a second load reflection factor c.sub.off
into the second input E.sub.2 in the first operating state off. The
T-section T has a third load reflection factor c.sub.on into the
second input E.sub.2 in the second operating state on. The first
load reflection factor a.sub.on is set to a first initial value.
The second load reflection factor c.sub.on is set to a second
initial value.
[0201] The circuit has a first matching network M.sub.1 with a
first connection A.sub.1 and a second connection A.sub.2. The first
connection A.sub.1 of the first matching network M.sub.1 is
connected to the first input E.sub.1 of the T-section T. The second
connection A.sub.2 of the first matching network M.sub.1 is
connected to the first source output QA.sub.1. The first matching
network M.sub.1 has a transformed first source reflection factor
b.sub.off' into the first connection A.sub.1 in the first operating
state off. The first matching network M.sub.1 has a transformed
first load reflection factor a.sub.on' into the second connection
A.sub.2 in the second operating state on.
[0202] The circuit has a second matching network M.sub.2 with a
third connection A.sub.3 and a fourth connection A.sub.4. The third
connection A.sub.3 of the second matching network M.sub.2 is
connected to the second input E.sub.2 of the T-section T. The
fourth connection (A4) of the second matching network M.sub.2 is
connected to the second source output QA.sub.2. The second matching
network M.sub.2 has a transformed second load reflection factor
c.sub.off' into the fourth connection A.sub.4 in the first
operating state off. The second matching network M.sub.2 has a
transformed third load reflection factor c.sub.on' into the fourth
connection A.sub.4 in the second operating state on.
[0203] A first value a.sub.on'.sub.opt of the transformed first
load reflection factor a.sub.on' is determined for optimizing a
parameter G.sub.1 of the circuit--such as is shown in FIG. 2, for
example--by measurement in the second operating state on. In
addition, a second value c.sub.off'.sub.opt of the transformed
second load reflection factor c.sub.off' is determined for
optimizing the parameter G.sub.1 of the circuit by measurement in
the first operating state off. In addition, a third value
c.sub.on'.sub.opt of the transformed third load reflection factor
c.sub.on' is determined for optimizing the parameter G.sub.1 of the
circuit by measurement in the second operating state on.
[0204] Of course, the exemplary embodiment in FIG. 12 allows for
applications and insights extending far beyond the specific
embodiment. Thus, the method in the exemplary embodiment in FIG.
12, in combination with load modulation, allows an equivalent
substitution of the load reflection factor acting at the second
input E.sub.1 of the T-section T (as the reflection factor of a
parallel circuit of the load impedance with an impedance
corresponding to a point on the first circle) by an effective load
reflection factor at the first input E.sub.1 of the T-section T
that results from the influence of the load modulation due to the
signal from the first source element Q.sub.1, in order to
significantly enlarge the area of application of the exemplary
embodiment in FIG. 12 yet further.
[0205] FIG. 13 shows a first distance P.sub.1. The first distance
P.sub.1 between the first value a.sub.on'.sub.opt and the complex
conjugate b.sub.off* of the first source reflection factor
b.sub.off is determined by:
P 1 = arctan h ( a on ' opt - b off * 1 - b off * a on ' opt * ) (
29 ) ##EQU00025##
[0206] Here, b.sub.off is the first source reflection factor
b.sub.off, b.sub.off* is the complex conjugate b.sub.off* of the
first source reflection factor b.sub.off, a.sub.on'.sub.opt is the
first value a.sub.on'.sub.opt of the transformed first load
reflection factor a.sub.on', and P.sub.1 is the first distance
P.sub.1.
[0207] In FIG. 13, a first circle K.sub.1 is shown. The first
circle K.sub.1 is determined as the set of all points at a first
distance P.sub.1 from the complex conjugate a.sub.on* of the first
load reflection factor a.sub.on by:
P ( y , a on * ) = arctan h ( y - a on * 1 - y * a on * ) .ident. P
1 ( 30 ) ##EQU00026##
[0208] Here, y is a point on the first circle K.sub.1, y* is the
complex conjugate y* of the point y on the first circle K.sub.1,
a.sub.on* is the complex conjugate a.sub.on* of the first load
reflection factor a.sub.on, and P.sub.1 is the first distance
P.sub.1.
[0209] FIG. 13 shows a modified first circle K.sub.1'. The modified
first circle K.sub.1' is determined as the set of all modified
reflection factors y'. In this context, an overall impedance is
associated with each of the modified reflection factors y', wherein
each overall impedance is determined from a first parallel circuit
of a load impedance of the load (L) and an impedance associated
with a reflection factor y on the first circle K.sub.1, wherein the
load impedance is associated with the load input reflection factor
r of the load L. The following applies here:
y'=y.parallel..GAMMA. (31)
[0210] In FIG. 14, a third distance P.sub.3 is shown. The third
distance P.sub.3 between the second value c.sub.off'.sub.opt and
the third value c.sub.on'.sub.opt is determined by:
P 3 = arctan h ( c on ' opt - c off ' opt 1 - c on ' opt * c off '
opt ) ( 32 ) ##EQU00027##
[0211] Here, c.sub.off'.sub.opt is the second value
c.sub.off'.sub.opt of the transformed second load reflection factor
c.sub.off', c.sub.on'.sub.opt is the third value c.sub.on'.sub.opt
of the transformed third load reflection factor c.sub.on', and
c.sub.on'.sub.opt* is the complex conjugate c.sub.on'.sub.opt* of
the third value c.sub.on'.sub.opt of the transformed third load
reflection factor c.sub.on'.
[0212] In FIG. 14, a third circle K.sub.3 is shown. The third
circle K.sub.3 is determined as the set of all points at the third
distance P.sub.3 from the third load reflection factor c.sub.on
by:
P ( z , c on ) = arctan h ( z - c on 1 - z * c on ) .ident. P 3 (
33 ) ##EQU00028##
[0213] Here, z is a point on the third circle K.sub.3, z* is the
complex conjugate z* of the point z on the third circle K.sub.3,
c.sub.on is the third load reflection factor c.sub.on, c.sub.on* is
the complex conjugate c.sub.on* of the third load reflection factor
c.sub.on, and P.sub.3 is the third distance P.sub.3.
[0214] In FIG. 14, two fourth values c.sub.off,1, c.sub.off,2 are
shown as points of intersection between the third circle K.sub.3
and the modified first circle K.sub.1'. At least one fourth value
c.sub.off,1, c.sub.off,2 of the second load reflection factor
c.sub.off is determined. Here, for the at least one fourth value
c.sub.off,1, c.sub.off,2 a sum of squares of the distances between
the fourth value c.sub.off,1, c.sub.off,2 and the third circle
K.sub.3 and between the fourth value c.sub.off,1, c.sub.off,2 and
the modified first circle K.sub.1' is minimized. In the exemplary
embodiment in FIG. 14, the distances are minimal (zero) at the
points of intersection.
[0215] A fifth value b.sub.off'.sub.1, b.sub.off'.sub.2 of the
transformed first source reflection factor b.sub.off' is determined
for each fourth value c.sub.off,1, c.sub.off,2 of the second load
reflection factor c.sub.off. In this process, a fourth impedance is
determined, wherein the fourth impedance is associated with the
fourth value c.sub.off,1, c.sub.off,2 of the second load reflection
factor c.sub.off. A fifth impedance is determined so that a second
parallel circuit of the fifth impedance with the load impedance is
equal to the fourth impedance, with the fifth value
b.sub.off'.sub.1, b.sub.off'.sub.2 of the transformed first source
reflection factor b.sub.off' being associated with the fifth
impedance.
[0216] The first matching network M.sub.1 of the exemplary
embodiment in FIG. 12 is determined below using the first load
reflection factor a.sub.on, and the first value a.sub.on'.sub.opt
of the transformed first load reflection factor a.sub.on', and the
first source reflection factor b.sub.off, and the fifth value
b.sub.off'.sub.1, b.sub.off'.sub.2 of the transformed first source
reflection factor b.sub.off'.
[0217] The second matching network M.sub.2 of the exemplary
embodiment in FIG. 12 is determined below using the second value
c.sub.off'.sub.opt of the transformed second load reflection factor
c.sub.off', and the third value c.sub.on'.sub.opt of the
transformed third load reflection factor c.sub.on', and the third
load reflection factor c.sub.on, and the fourth value c.sub.off,1,
c.sub.off,2 of the second load reflection factor c.sub.off.
[0218] The input quantities of the method in the exemplary
embodiment in FIG. 12 are, firstly, measurable quantities: The
first source reflection factor b.sub.off, the load input reflection
factor .GAMMA., as well as, typically determined in load pull
measurements, the first value a.sub.on'.sub.opt of the transformed
first load reflection factor a.sub.on', which optimizes the source
and circuit characteristics in the second operating state on, the
second value c.sub.off'.sub.opt of the transformed second load
reflection factor c.sub.off', which optimizes the source and
circuit characteristics in the first operating state off, and the
third value c.sub.on'.sub.opt of the transformed third load
reflection factor c.sub.on', which optimizes the source and circuit
characteristics in the second operating state on.
[0219] Additional input quantities of the method in the exemplary
embodiment in FIG. 12 are the quantities of the first load
reflection factor a.sub.on and third load reflection factor
c.sub.on, which are determined independently in the second
operating state on of the circuit.
[0220] Proceeding from the aforementioned input quantities, the
method is used to determine the pairs of mathematical
transformation properties--a maximum of two pairs aside from
pathological cases--that are compatible with the input
quantities.
[0221] The mathematical transformation properties determined permit
largely lossless, non-reciprocal matching networks that exhibit the
mathematical transformation properties that have been determined.
One example for the design of a reciprocal, largely lossless
matching network, proceeding from known transformation properties,
is found in an approach for the matching network in the form of an
adequately flexible circuit topology--for example, a number of
series-connected microstriplines whose particular trace widths and
lengths are unspecified--with subsequent numerical optimization of
the trace widths and lengths.
[0222] The mathematical transformation properties determined for
the exemplary embodiment in FIG. 12 also make it possible to
determine the transformed source reflection factors b.sub.on',
d.sub.on' from the source reflection factors b.sub.on, d.sub.on of
the first and second source elements Q.sub.1, Q.sub.2 in the second
operating state on of the circuit, which are accessible from the
measurement. Together with the load input reflection factor
.GAMMA., all termination conditions for the T-section T are thus
known.
[0223] Methods are available--for example, circuit simulation with
S-parameter ports--for determining the transformation properties of
a T-section T that is assumed to be ideal or is implemented in
microstrip technology from its termination conditions, e.g., in the
form of a scattering matrix.
[0224] Moreover, the knowledge of the scattering matrix makes it
possible to superpose a first forward time-domain sinusoidal signal
coming from the first output A.sub.1 and a second forward
time-domain sinusoidal signal coming from the third output A.sub.3
at the T-section T, and to specify a first time-domain sinusoidal
signal reflected from the first input E.sub.1 and a second
time-domain sinusoidal signal reflected from the second input
E.sub.2. Here, the first and the second forward time-domain
sinusoidal signals have the same frequency for a given relative
phase position and a given amplitude ratio between the first and
the second forward time-domain sinusoidal signals. The forward and
reflected time-domain sinusoidal signals are in turn transformed
into new, so-called effective load reflection factors
a.sub.on,{tilde over (c)}.sub.on, which may match or differ from
the respective load reflection factors a.sub.on, c.sub.on that were
determined independently at the outset.
[0225] For each given relative phase position and each given
amplitude ratio between the first and the second forward
time-domain sinusoidal signals, the superposition loss of the two
signals at the T-section T can be determined. The superposition
loss is the difference between the power output to the load and the
sum of the powers of the forward time-domain sinusoidal signals.
Accordingly, it is possible to determine for each given amplitude
ratio a singular relative phase position between the first and the
second forward time-domain sinusoidal signals that minimizes the
superposition loss, including the effective load reflection factors
associated with this singular relative phase position.
[0226] Using FIG. 20 and FIG. 21, an example for determining the
singular relative phase position and the associated effective load
reflection factors is described below, starting from the
termination conditions of the T-section and the amplitudes and
relative phase position of the forward time-domain sinusoidal
signals. The example makes use of a simulation program. The
simulation program makes a widely used tool available for
high-frequency circuit engineering. Among other things, the
simulation program offers as a predefined circuit element a
circulator for which different reference impedances can be chosen
at the three inputs, hereinafter called a three-port circulator.
The three-port circulator of the simulation program is thus an
ideal impedance-transforming component.
[0227] FIG. 20 shows a first equivalent circuit for the terminated
T-section T, which is used below in determining the effective load
reflection factors ona.sub.on,{tilde over (c)}.sub.on. The first
equivalent circuit contains a first three-port circulator Z.sub.1
and a second three-port circulator Z.sub.2.
[0228] The first three-port circulator Z.sub.1 has a first
circulator port A.sub.1', a second circulator port A.sub.m1, and a
third circulator port A.sub.m2. The first three-port circulator
Z.sub.1 exhibits the first transformed source reflection factor
b.sub.on' into the first circulator port A.sub.1'.
[0229] The second three-port circulator Z.sub.2 has a fourth
circulator port A.sub.3', a fifth circulator port A.sub.m3, and a
sixth circulator port A.sub.m4. The second three-port circulator
Z.sub.2 exhibits the third transformed source reflection factor
d.sub.on' into the fourth circulator port A.sub.3'.
[0230] The first equivalent circuit contains a T-section T. The
T-section T has a first input E.sub.1, a second input E.sub.2, and
a third input E.sub.3. The first input E.sub.1 is connected to the
first circulator port A.sub.1' and is accordingly terminated with
the first transformed source reflection factor b.sub.on'. The
second input E.sub.1 is connected to the fourth circulator port
A.sub.3' and is accordingly terminated with the third transformed
source reflection factor d.sub.on'. The third input E.sub.3 is
terminated with the load reflection factor F. The T-section T can
be implemented as a line node or as a microstrip T-section, for
example.
[0231] In technical terms, the termination of the first input
E.sub.1 is implemented with the first transformed source reflection
factor b.sub.on' through the selection of an impedance associated
with the first transformed source reflection factor b.sub.on' as
reference impedance for the first three-port circulator Z.sub.1 at
the first circulator port A.sub.1'. In the exemplary embodiment in
FIG. 20, a value of 50.OMEGA. is chosen for each of the reference
impedances for the first three-port circulator Z.sub.1 at the
second circulator port A.sub.m1 and at the third circulator port
A.sub.m2.
[0232] In technical terms, the termination of the second input
E.sub.2 is implemented with the third transformed source reflection
factor d.sub.on' through the selection of an impedance associated
with the third transformed source reflection factor d.sub.on' as
reference impedance for the second three-port circulator Z.sub.1 at
the fourth circulator port A.sub.3'. In the exemplary embodiment in
FIG. 20, a value of 50.OMEGA. is chosen for each of the reference
impedances for the second three-port circulator Z.sub.1 at the
fifth circulator port A.sub.m3 and at the sixth circulator port
A.sub.m4.
[0233] A first time-domain sinusoidal signal of a given frequency,
phase, and amplitude is applied to the second circulator port
A.sub.m1, and a second time-domain sinusoidal signal of the given
frequency with a given relative phase with respect to the phase of
the first time-domain sinusoidal signal and a given relative
amplitude with respect to the amplitude of the first time-domain
sinusoidal signal is applied to the fifth circulator port
A.sub.m3.
[0234] In the simulation, a first reflected current is measured at
the third circulator port A.sub.m2, and the third circulator port
A.sub.m2 is terminated reflection-free. In the simulation, a first
effective current and a first effective voltage are accessed at the
first circulator port A.sub.1'.
[0235] In the simulation, a second reflected current is measured at
the sixth circulator port A.sub.m4, and the sixth circulator port
A.sub.m4 is terminated reflection-free. In the simulation, a second
effective current and a second effective voltage are accessed at
the fourth circulator port A.sub.3'.
[0236] A first effective load reflection factor a.sub.on from the
relative phase and the relative amplitude and a second effective
load reflection factor {tilde over (c)}.sub.on from the relative
phase and the relative amplitude are determined using the first
equivalent circuit from FIG. 20 and a second equivalent circuit
from FIG. 21, with said first effective load reflection factor
a.sub.on acting into the first input E.sub.1 and said second
effective load reflection factor {tilde over (c)}.sub.on acting
into the second input E.sub.2.
[0237] FIG. 21 shows a second equivalent circuit for the terminated
T-section, which is used below in determining the effective load
reflection factors a.sub.on,{tilde over (c)}.sub.on. The second
equivalent circuit contains a third three-port circulator Z.sub.3,
a fourth three-port circulator Z.sub.4, a fifth three-port
circulator Z.sub.5, and a sixth three-port circulator Z.sub.6.
[0238] The third three-port circulator Z.sub.3 has a seventh
circulator port A.sub.1'', an eighth circulator port A.sub.m1', and
a ninth circulator port A.sub.m2'. The third three-port circulator
Z.sub.3 exhibits the first transformed source reflection factor
b.sub.on' into the seventh circulator port A.sub.1''.
[0239] The fourth three-port circulator Z.sub.4 has a tenth
circulator port A.sub.3'', an eleventh circulator port A.sub.m3',
and a twelfth circulator port A.sub.m4'. The fourth three-port
circulator Z.sub.4 exhibits the third transformed source reflection
factor d.sub.on' into the tenth circulator port A.sub.3''.
[0240] The fifth three-port circulator Z.sub.5 has a thirteenth
circulator port A.sub.5, a fourteenth circulator port A.sub.m5, and
a fifteenth circulator port A.sub.m6. The fifth three-port
circulator Z.sub.5 exhibits a first variable effective load
reflection factor a.sub.on' into the thirteenth circulator port
A.sub.5.
[0241] The sixth three-port circulator Z.sub.6 has a sixteenth
circulator port A.sub.6, a seventeenth circulator port A.sub.m7,
and an eighteenth circulator port A.sub.m8. The sixth three-port
circulator Z.sub.6 exhibits a second variable effective load
reflection factor {tilde over (c)}.sub.on' into the sixteenth
circulator port A.sub.6.
[0242] In technical terms, the property of the third three-port
circulator Z.sub.3 of exhibiting the first transformed source
reflection factor b.sub.on' into the seventh circulator port
A.sub.1'' is implemented through the selection of an impedance
associated with the first transformed source reflection factor
b.sub.on' as reference impedance for the third three-port
circulator Z.sub.3 at the seventh circulator port A.sub.1''. In the
exemplary embodiment in FIG. 21, a value of 50.OMEGA. is chosen for
each of the reference impedances for the third three-port
circulator Z.sub.3 at the eighth circulator port A.sub.m1' and at
the ninth circulator port A.sub.m2'.
[0243] In technical terms, the property of the fourth three-port
circulator Z.sub.4 of exhibiting the third transformed source
reflection factor d.sub.on' into the tenth circulator port
A.sub.3'' is implemented through the selection of an impedance
associated with the third transformed source reflection factor
d.sub.on' as reference impedance for the fourth three-port
circulator Z.sub.4 at the tenth circulator port A.sub.3''. In the
exemplary embodiment in FIG. 21, a value of 50.OMEGA. is chosen for
each of the reference impedances for the fourth three-port
circulator Z.sub.4 at the eleventh circulator port A.sub.m1' and at
the twelfth circulator port A.sub.m4'.
[0244] A value of 50.OMEGA. is chosen for each of the reference
impedances for the fifth three-port circulator Z.sub.5 at the
fourteenth circulator port A.sub.m5 and at the fifteenth circulator
port A.sub.m6. A value of 50.OMEGA. is chosen for each of the
reference impedances for the sixth three-port circulator Z.sub.6 at
the seventeenth circulator port A.sub.m7 and at the eighteenth
circulator port A.sub.m8.
[0245] A signal equal to the first time-domain sinusoidal signal is
applied at the eighth circulator port A.sub.m1', and a signal equal
to the second time-domain sinusoidal signal is applied at the
eleventh circulator port A.sub.m3'.
[0246] In the simulation, a third reflected current is measured at
the ninth circulator port A.sub.m2', and the ninth circulator port
A.sub.m2' is terminated reflection-free. In the simulation, a third
effective current and a third effective voltage are accessed at the
seventh circulator port A.sub.1''.
[0247] In the simulation, a fourth reflected current is measured at
the twelfth circulator port A.sub.m4', and the sixth circulator
port A.sub.m4 is terminated reflection-free. In the simulation, a
fourth effective current and a fourth effective voltage are
accessed at the tenth circulator port A.sub.3''.
[0248] The fourteenth circulator port A.sub.m5, the fifteenth
circulator port A.sub.m6, the seventeenth circulator port A.sub.m7,
and the eighteenth circulator port A.sub.m8 are terminated
reflection-free.
[0249] In a simulation of the first equivalent circuit, values for
the first forward current, the second forward current, the first
effective voltage, the second effective voltage, the first
effective current, and the second effective current are
obtained.
[0250] In simulations of the second equivalent circuit, the first
variable effective load reflection factor a.sub.on' and the second
variable effective load reflection factor {tilde over (c)}.sub.on'
are optimized such that:
[0251] the third reflected current is equal in magnitude and
direction to the first reflected current,
[0252] the fourth reflected current is equal in magnitude and
direction to the second reflected current,
[0253] the third effective current is equal in magnitude and
direction to the first effective current,
[0254] the fourth effective current is equal in magnitude and
direction to the second effective current,
[0255] the third effective voltage is equal in magnitude to the
first effective voltage, and
[0256] the fourth effective voltage is equal in magnitude to the
second effective voltage.
[0257] The value found by means of the optimization for the first
variable effective load reflection factor a.sub.on' then matches
the value sought for the first effective load reflection factor
a.sub.on, and the value found by means of the optimization for the
second variable effective load reflection factor {tilde over
(c)}.sub.on' matches the value sought for the first effective load
reflection factor {tilde over (c)}.sub.on.
[0258] The effective reflection factors acting into the first input
E.sub.1 and the second input E.sub.2 are determined from the
termination conditions at the inputs E.sub.1, E.sub.2, E.sub.3 of
the T-section T and the input signals at all three inputs E.sub.1,
E.sub.2, E.sub.3 of the T-section T--of which, in the exemplary
embodiment in FIGS. 20 and 21, the input signal entering the third
input E.sub.3 of the T-section T has zero magnitude.
[0259] The comparison of the sum of the power of the first
time-domain sinusoidal signal and the power of the second
time-domain sinusoidal signal with the power output at the third
input E.sub.3 of the T-section T provides a method for determining
the summation loss in the T-section T, in particular as a function
of the relative phase.
[0260] In one possible application, efforts are made to minimize
the summation loss. This is accomplished by repeating the method
for different values of the relative phase so as to arrive at a
singular relative phase position through which the summation loss
is minimized.
[0261] For example, if an amplitude ratio is provided through a
ratio of the compression points of both source elements, then the
method from the exemplary embodiment teaches the determination,
from a first pair of independently determined load reflection
factors, of a new pair of load reflection factors in the form of
the pair of effective load reflection factors associated with the
singular relative phase position, and thus permits an improvement
over a first pair of load reflection factors by a derived second
pair of load reflection factors.
[0262] As compared to the method of pure trial and error, this is,
for example, the successive execution of a large number of
iterations. For such a continued iteration, the great iteration
theorem suggests the existence of a fixed point pair, both of whose
pair points lie within the closed unit disk in the reflection
factor plane. The iteration is dependent on a pair of load
reflection factors as an initial value. According to the great
iteration theorem, the iteration converges to the fixed point pair
with every pair of load reflection factors as the starting point.
However, the design method for Doherty amplifiers, as a special
case of the load-modulation amplifier, provides an obvious pair of
load reflection factors as an initial value (at least for real load
input reflection factors). As an initial value, the obvious pair of
load reflection factors in both entries is the reflection factor
associated with twice the load impedance.
[0263] Thus, the above-described method teaches, in particular, the
reaching of a closed solution for the singular phase position, the
minimal summation losses, and the effective load reflection factors
associated therewith from measurable input quantities--the first
source reflection factor b.sub.off in the first operating state
off, the source reflection factors b.sub.on, d.sub.on of the first
source element Q.sub.1 and the second source element Q.sub.2 in the
second operating state on, the load input reflection factor
.GAMMA., and the first value a.sub.on'.sub.opt, the second value
c.sub.off'.sub.opt, and the third value c.sub.on'.sub.opt--as well
as reaching the associated pair of two mathematically permissible
transforming actions of the first and the second matching network
M.sub.1, M.sub.2.
[0264] FIG. 22 shows another exemplary embodiment of a circuit that
is being designed. The circuit has a first source element Q.sub.1
with a first source output QA.sub.1 and with a first source
reflection factor b. The circuit has a second source element
Q.sub.2 with a second source output QA.sub.2 and with a second
source reflection factor d. The circuit also has a load L.
[0265] The circuit has a T-section T with a first input E.sub.1, a
second input E.sub.2, and an output E.sub.3. The T-section T has a
first load reflection factor a into the first input E.sub.1, as is
shown schematically in FIG. 22 by means of an arrow. The T-section
T has a second load reflection factor c into the second input
E.sub.2, as is likewise shown schematically in FIG. 22 by means of
an arrow. In the exemplary embodiment in FIG. 22, the output
E.sub.3 of the T-section T is connected to the load L.
[0266] The circuit has a first matching network M.sub.1 with a
first connection A.sub.1 and a second connection A.sub.2. The
second connection A.sub.2 is connected to the first source output
QA.sub.1. The first connection A.sub.1 is connected to the first
input E.sub.1 of the T-section T. By means of the first matching
network M.sub.1, a transformed first load reflection factor a' is
achieved into the second connection A.sub.2 and a transformed first
source reflection factor b' is achieved into the first connection
A.sub.1. The transformed first load reflection factor a' and the
transformed first source reflection factor b' are shown
schematically in FIG. 22 by means of arrows.
[0267] The circuit has a second matching network M.sub.2 with a
third connection A.sub.3 and a fourth connection A.sub.4. The
fourth connection A.sub.4 is connected to the second source output
QA.sub.2. The third connection A.sub.3 is connected to the second
input E.sub.2 of the T-section T. By means of the second matching
network M.sub.2, a transformed second load reflection factor c' is
achieved into the fourth connection A.sub.4. Moreover, by means of
the second matching network M.sub.2, a transformed second source
reflection factor d' is achieved into the third connection A.sub.3.
The transformed second load reflection factor c' and the
transformed second source reflection factor d' are shown
schematically in FIG. 22 by means of arrows.
[0268] In FIG. 22, a first value a'.sub.opt of the transformed
first load reflection factor a' and a second value c'.sub.opt of
the transformed second load reflection factor c' are shown
schematically by means of arrows. In one method, the first value
a'.sub.opt of the transformed first load reflection factor a' is
determined. In this method, the first source element Q.sub.1 has a
first optimum Max.sub.1 of a first parameter G.sub.1 for the first
value a'.sub.opt of the transformed first load reflection factor a'
acting at the first source output QA.sub.1, as is shown
schematically by way of example in FIG. 24. The first value
a'.sub.opt of the transformed first load reflection factor a'
differs from the complex conjugate of the first source reflection
factor b here.
[0269] In one method, the second value c'.sub.opt of the
transformed second load reflection factor c' is determined. In this
method, the second source element Q.sub.2 has a second optimum
Max.sub.2 of a second parameter G.sub.2 for the second value
c'.sub.opt of the transformed second load reflection factor c'
acting at the second source output QA.sub.2, as is shown
schematically by way of example in FIG. 25. Here, the second value
c'.sub.opt of the transformed second load reflection factor c'
differs from the complex conjugate of the second source reflection
factor d.
[0270] FIG. 23 shows a distance value P.sub.aus, and a third value
a'.sub.est of the transformed first load reflection factor a', and
a fourth value c'.sub.est of the transformed second load reflection
factor c'. These values are determined in a method explained below.
In this method, the distance value P.sub.aus, and the third value
a'.sub.est of the transformed first load reflection factor a', and
the fourth value c'.sub.est of the transformed second load
reflection factor c' are determined by the means that a first
distance P.sub.1, and a second distance P.sub.2, and a third
distance P.sub.3, and a fourth distance P.sub.4 are determined. The
distances P.sub.1, P.sub.2, P.sub.3, and P.sub.4 are shown
schematically in FIG. 23.
[0271] A first distance P.sub.1 between the first value a'.sub.opt
and the transformed first load reflection factor a' is defined
by:
P 1 = arc tan h ( a opt ' - a ' 1 - a ' * a opt ' ) ( 34 )
##EQU00029##
[0272] Here, P.sub.1 is the first distance P.sub.1, a' is the
transformed first load reflection factor a', a'* is the complex
conjugate a' of the transformed first load reflection factor a',
and a'.sub.opt is the first value a'.sub.opt.
[0273] A second distance P.sub.2 between the second value
c'.sub.opt and the transformed second load reflection factor c' is
defined by:
P 2 = arc tan h ( c opt ' - c ' 1 - c ' * c opt ' ) ( 35 )
##EQU00030##
[0274] Here, P.sub.2 is the second distance P.sub.2, c' is the
transformed second load reflection factor c', c'* is the complex
conjugate c'* of the transformed second load reflection factor c',
and c'.sub.opt is the second value c'.sub.opt.
[0275] A third distance P.sub.3 between the transformed first load
reflection factor a' and the complex conjugate b* of the first
source reflection factor b is defined by:
P 3 = arc tan h ( a ' - b * 1 - ba ' ) ( 36 ) ##EQU00031##
[0276] Here, P.sub.3 is the third distance P.sub.3, b is the first
source reflection factor b, b* is the complex conjugate b* of the
first source reflection factor b, and a' is the transformed first
load reflection factor a'.
[0277] A fourth distance P.sub.4 between the transformed second
load reflection factor c' and the complex conjugate d* of the
second source reflection factor d is defined by:
P 4 = arc tan h ( c ' - d * 1 - d c ' ) ( 37 ) ##EQU00032##
[0278] Here, P.sub.4 is the fourth distance P.sub.4, d is the
second source reflection factor d, d* is the complex conjugate d*
of the second source reflection factor d, and c' is the transformed
second load reflection factor c'.
[0279] The distance value P.sub.aus, and the third value
a'.sub.est, and the fourth value c'.sub.est are determined by the
means that a minimum of the geometric mean of the first distance
P.sub.1 and the second distance P.sub.2 is determined under the
boundary condition that the third distance P.sub.3 is equal to the
fourth distance P.sub.4 and is not zero. The minimum of the
geometric mean is determined by the means that the transformed
first load reflection factor a' and the transformed second load
reflection factor c' are varied, and the complex conjugate b* of
the first source reflection factor b, and the complex conjugate d*
of the second source reflection factor d, and the first value
a'.sub.opt, and the second value c'.sub.opt have a fixed value, as
is shown schematically in the exemplary embodiment in FIG. 23.
[0280] The value of the third distance P.sub.3 associated with the
minimum is set as the distance value P.sub.aus. The value of the
transformed first load reflection factor a' associated with the
minimum is set as the third value a'.sub.est. The value of the
transformed second load reflection factor c' associated with the
minimum is set as the fourth value c'.sub.est.
[0281] In FIG. 26, a first circle K.sub.1, and a second circle
K.sub.2, and a fifth value b'.sub.est, and a sixth value d'.sub.est
are shown schematically. The fifth value b'.sub.est of the
transformed first source reflection factor b' and the sixth value
d'.sub.est of the transformed second source reflection factor d'
are determined by the means that the first circle K.sub.1 with a
real center point that intersects a real reflection factor value of
1/3 and a real reflection factor value of -1 is determined. In
addition, the second circle K.sub.2 is determined as the set of all
points y with a distance from the real reflection factor value of
1/3 equal to the distance value P.sub.aus by:
P ( y , 1 3 ) = arc tan h ( y - 1 3 1 - y 1 3 ) .ident. P aus ( 38
) ##EQU00033##
[0282] Here, y is a point y on the second circle K.sub.2, and
P.sub.aus the distance value P.sub.aus of the third distance
P.sub.3.
[0283] The fifth value b'.sub.est is determined as equal to the
value of a first point of intersection between the first circle
K.sub.1 and the second circle K.sub.2, and the sixth value
d'.sub.est is determined as equal to the value of a second point of
intersection between the first circle K.sub.1 and the second circle
K.sub.2 different from the first point of intersection.
[0284] In the exemplary embodiment in FIG. 22, the first matching
network M.sub.1 is determined using the first source reflection
factor b, and the fifth value b'.sub.est of the transformed first
source reflection factor b', and the first load reflection factor
a, and the third value a'.sub.est of the transformed first load
reflection factor a'.
[0285] Moreover, in the exemplary embodiment in FIG. 22, the second
matching network M.sub.2 is determined using the second source
reflection factor d and the sixth value d'.sub.est of the
transformed second source reflection factor d' and the second load
reflection factor c and the fourth value c'.sub.est of the
transformed second load reflection factor c'.
[0286] In the exemplary embodiment in FIG. 22, two source elements
Q.sub.1, Q.sub.2 drive a common load L, each through a matching
network M.sub.1, M.sub.2 and the two inputs E.sub.1, E.sub.2 of a
T-section T. In this regard, the circuit situation of the exemplary
embodiment from FIG. 22 resembles the doubled use of the exemplary
embodiment in FIG. 1 in one circuit. As has already been the case
with the exemplary embodiment from FIG. 12, however, in the
exemplary embodiment in FIG. 22 the parameters G.sub.1, G.sub.2 on
which the optimization is based can likewise only be formulated as
a characteristic of the overall circuit under consideration.
[0287] Whereas in the exemplary embodiment in FIG. 12 an optimal
value of the second image impedance that is compatible with the
mathematical boundary conditions for reciprocal, lossless matching
networks M.sub.1, M.sub.2 is determined from, e.g., two fixed
counter-image impedances and one fixed image impedance, in the
exemplary embodiment in FIG. 22, proceeding from given source and
load impedances and a known optimal pair of transformed load
impedances, a pair of varied transformed load impedances is
determined that best approximates the optimal pair of transformed
load impedances, taking into account the mathematical limitations
due to the reciprocity and losslessness of the matching
networks.
[0288] For reasons of improved clarity, the exemplary embodiment in
FIG. 22 is described with the aid of a load L assumed to be real,
and with at least implicit reference to two source elements
Q.sub.1, Q.sub.2 of the same type that generate signals of equal
signal amplitude and frequency at the two inputs E.sub.1, E.sub.2
of the T-section T. Of course, the application of the embodiment of
the method described in the exemplary embodiment in FIG. 22 extends
mutatis mutandis to a considerably broader range of load reflection
factors, source elements, and source signals. In turn, the load
impedances can be effective load impedances that take into account
the influence of load modulation by the respective other signal
source.
[0289] All exemplary embodiments that will be explained are based
on a two-stage procedure: First, desirable pairs of image
impedances and counter-image impedances are determined, and
subsequently a direct attempt is made to synthesize a matching
network that maps the counter-image impedances onto the image
impedances. The method uses mathematical relationships for an
important class of matching networks (reciprocal, lossless) to
first derive an optimal transforming action of the matching network
being sought that is compatible with termination conditions, in
order to thereafter derive a suitable matching network, for example
from this transforming action.
[0290] The application of the method in the above-described
exemplary embodiments to two circuit topologies (series and
parallel circuits) that are significantly different from one
another, in two embodiments that are significantly different from
one another, spans the full range of application of the novel and
generally useful principle:
[0291] For the case of the series circuit, in the exemplary
embodiment in FIG. 9 both counter-image impedances and both image
impedances are in each case located on the same side of the
matching network, for example, while in the exemplary embodiment in
FIG. 1 one first counter-image impedance and one second image
impedance are located on one side of the matching network M.sub.1
but one second counter-image impedance and one first image
impedance are located on the opposite side of the matching network
M.sub.1.
[0292] For the case of the parallel circuit, the exemplary
embodiment in FIG. 12 shows the optimization of a load impedance
(or a transformed load impedance) with the other load impedance
(transformed load impedance) being held constant, while an optimal
pair of two variable transformed load impedances is determined
using the exemplary embodiment in FIG. 22.
[0293] If, as for example in FIG. 12 or FIG. 22, two source
elements Q.sub.1, Q.sub.2 operate in parallel with one another (for
example, through a T-section T) into the same load L, then a first
component of a signal coming from the first source element Q.sub.1
is reflected back into the first source element Q.sub.1, and a
second component goes into the load L, but a third component goes
into the output of the second source element Q.sub.2. The second
source element Q.sub.2 cannot distinguish, among the signal
components reaching it, between the signal component arising from
its own reflected signal and the signal component originating from
the first source element Q.sub.1. All that the second source
element Q.sub.2 experiences is another signal reflected to it. The
first source element Q.sub.1 thus modifies the load impedance
perceived by the second source element Q.sub.2. The load reflection
factor perceived by the second source element Q.sub.2, which is
associated with the perceived load impedance, can also be referred
to as the effective load reflection factor.
[0294] A transformation of a "physical" load reflection factor into
the "effective" load reflection factor is called load modulation
(or "active load pull"). When reference is made hereinafter to a
reflection factor that is measured into an input of a T-section T,
then this reflection factor can be a physical reflection factor or
an effective reflection factor unless explicitly specified.
[0295] A special case is the lossless addition of the output
signals of two identical source elements Q.sub.1, Q.sub.2 at the
symmetrical T-section T, as is explained in detail in the
description of the equivalent circuit diagrams from FIG. 12 ff.
[0296] The exemplary embodiments are explained for a simple
understanding of real effective load reflection factors. Since
every impedance can be represented with both a real and a complex
reflection factor through an appropriate selection of a complex
reference impedance, the simplification for real effective load
reflection factors takes place without restricting generality:
Accordingly, applicability of the method is not restricted to real
impedances on account of the explanation using real reflection
factors.
[0297] The operation of complex conjugation is indicated in the
formulas by appending an asterisk to a quantity to be conjugated.
For example, the complex conjugate of a is a*. Except where
explicitly stated otherwise, the following description of the
exemplary embodiments is directed to power-preserving, reciprocal
matching networks M.sub.1, M.sub.2.
[0298] Except where explicitly stated otherwise, a matching network
M.sub.1, M.sub.2 is hereinafter provided as a circuit section with
a first connection A.sub.1--for example, as output--and a second
connection A.sub.2--for example, as input. An arbitrary direction
of passage (here, for a signal wave)--typically defined from the
source element to the load--through the matching network M.sub.1,
M.sub.2--for example, from the input to the output--is referred to
hereinafter as the forward direction. The opposite direction of
passage is referred to as the reverse direction. A matching network
M.sub.1, M.sub.2 traversed in the reverse direction is referred to
as the reverted matching network associated with this matching
network M.sub.1, M.sub.2.
[0299] If the transforming action of a matching network M.sub.1,
M.sub.2 is mathematically described by a function f, which operates
on the reflection factor plane, then f is called the describing
function of the matching network M.sub.1, M.sub.2. A describing
function f.sup.R of the reverted matching network is called the
reverted describing function f.sup.R.
[0300] In cases where an extreme of the parameter serves as the
optimum, the extremal property changes from "minimal" to "maximal"
and vice versa with an additional factor of -1 in the definition of
the parameter. The designation (Max) for the maximum as optimum in
an exemplary embodiment is accordingly a minimum (Min) as optimum
in a different exemplary embodiment without a detailed explanation
being required.
[0301] The designation chosen hereinafter for individual
quantities, such as "load reflection factor" and "source reflection
factor," or "load element" and "source element," does not specify
in a restrictive manner how the designated quantities are arranged
in a specific arrangement relative to one another in the direction
of signal flow or opposite to the direction of a signal flow in the
circuit under discussion.
[0302] In order to be able to refer explicitly to a non-Euclidean
nature of a distance under consideration when specifying geometric
quantities that have the nature of a distance or are determined by
distance, a radius is referred to as a "Poincare radius" for
example, and a circle as a "Poincare circle," when the circle is
the locus of all points at a fixed Poincare distance--equal to the
Poincare radius--from a center point.
[0303] As is evident using the symmetry of the transformation paths
in the Smith chart, for a non-resistive, reciprocal matching
network M.sub.1, M.sub.2 with a load input and a source input,
freedom from reflection with respect to a real load L at the load
output A.sub.1 of the matching network M.sub.1 is equivalent to
complex conjugate matching at the source input A.sub.2 of the
matching network M.sub.1.
[0304] In general, for a series circuit having two circuit elements
Q.sub.1 or Q.sub.2 and L connected together by a matching network
M.sub.1, M.sub.2, it is only possible in special cases to design
the matching network M.sub.1, M.sub.2 such that the input
reflection factor of the first circuit element in a first direction
relative to the signal flow is mapped by the matching network
M.sub.1, M.sub.2 to a load reflection factor that is as optimally
matched as possible for the second circuit element, while an output
reflection factor of the second circuit element in a second
direction relative to the signal flow is simultaneously mapped by
the matching network M.sub.1, M.sub.2, traversed in the reverse
direction, to a source reflection factor that is as optimally
matched as possible for the first circuit element.
[0305] In general, impedances and reflection factors are
complex-valued; accordingly, every impedance value/reflection
factor value is uniquely specified by specifying two real degrees
of freedom. The aforementioned mathematical boundary conditions for
the transforming action of reciprocal, lossless matching networks
M.sub.1, M.sub.2 are such that a single real degree of freedom for
the transforming action of the matching network M.sub.1, M.sub.2
remains after specifying a counter-image impedance and an image
impedance under the transformation of the matching network M.sub.1,
M.sub.2 traversed in one direction. This is not enough to be able
to freely specify the image impedance for a second counter-image
impedance under the matching network M.sub.1, M.sub.2 traversed in
the same direction or the opposite direction. In fact, as explained
below, the second image impedance value is restricted to the
boundary of a circle.
[0306] In a method for designing an electronic circuit, two pairs
of counter-image impedances and image impedances that are optimal
within the scope of the mathematical boundary conditions under a
reciprocal, non-resistive matching network M.sub.1, M.sub.2 are
sought, wherein the mapping of one counter-image impedance onto the
associated image impedance by means of the matching network
M.sub.1, M.sub.2 takes place in a first direction, and the mapping
of the second counter-image impedance onto the associated image
impedance takes place in the opposite direction.
[0307] A series circuit of two circuit elements connected together
by a matching network M.sub.1, M.sub.2 is likewise possible. Two
pairs of counter-image impedances and image impedances that are
optimal within the scope of the mathematical boundary conditions
under a reciprocal, non-resistive matching network M.sub.1, M.sub.2
are sought, wherein the mapping of both counter-image impedances
onto the respective associated image impedances by means of the
matching network M.sub.1, M.sub.2 takes place in the same direction
of traversal.
[0308] The method for designing an electronic circuit can be
applied to a circuit topology in which the signals of two source
elements Q.sub.1, Q.sub.2 are conducted to a common load L through
a T-section T.
[0309] The fundamentals common to the explained exemplary
embodiments are explained in detail below.
[0310] The Schwarz-Pick Theorem
[0311] In circuit design, it is frequently necessary to match the
impedance levels of subassemblies or components that follow one
another in the signal path. This is the task of separate,
interposed functional blocks, the so-called matching networks,
e.g., M.sub.1, M.sub.2 in FIG. 12.
[0312] FIG. 1 shows an electronic circuit in the form of a chain
having a first amplifier as source element Q.sub.1 with a source
reflection factor b.sub.on, a first matching network M.sub.1 with a
first connection A.sub.1 and a second connection A.sub.2, and, for
example, a second amplifier as load element L with a load
reflection factor a.sub.on, wherein the first connection A.sub.1 is
connected to the load element L and the second connection A.sub.2
is connected to the first source element Q.sub.1. With the aid of
the matching network M.sub.1, a transformed first load reflection
factor a.sub.on' into the matching network M.sub.1 measured at the
second connection A.sub.2 is achieved, and a transformed first
source reflection factor b.sub.on' into the first matching network
M.sub.1 at the first connection A1 is achieved.
[0313] The design of the matching network M1 from reactive elements
within the amplifier chain Q1, L, as is shown in the form of the
circuit 1 in FIG. 1, is based on the following assumption: If the
matching network M.sub.1 maps the source reflection factor b.sub.on
onto a given transformed first source reflection factor
b.sub.on'--wherein, e.g., an efficiency of the power gain of the
load element L can be optimized by a desired given transformed
first source reflection factor b.sub.on', for example--then the
transformed first load reflection factor a.sub.on' that the source
element Q.sub.1 experiences lies on a circle in the Smith chart,
hereinafter referred to as the load circle. The load circle does
not depend on the specific first matching network M.sub.1, but
instead depends (for a given first source reflection factor
b.sub.on) only on the transformed first source reflection factor
b.sub.on' of the first amplifier stage Q.sub.1 and the first load
reflection factor a.sub.on (i.e., the input reflection factor of
the second amplifier stage).
[0314] In the course of further investigations by the applicant, it
has been shown that the counter-image of the load circle also
represents a circle in the Smith chart, hereinafter referred to as
the counter-image circle, among the set of all reciprocal, lossless
matching networks that map the given source reflection factor
b.sub.on onto the given transformed source reflection factor
b.sub.on' for a given first load reflection factor a.sub.on.
[0315] In general, the transforming action of electronic matching
networks M.sub.1, M.sub.2 is described mathematically by Mobius
transformations. One property of Mobius transformations is the
preservation of circles: circles are always mapped onto circles, in
particular the mapping of the counter-image circle onto the load
circle:
[0316] Every point on the counter-image circle is mapped onto a
point on the load circle by all reciprocal, lossless matching
networks M.sub.1, M.sub.2, that map the given source reflection
factor b.sub.on onto the given transformed source reflection factor
b.sub.on'.
[0317] In the course of further investigations by the applicant,
the application of a theorem of function theory in the field of
electrical engineering has been developed:
[0318] The Schwarz-Pick theorem. If f:D|.fwdarw.D| is a holomorphic
mapping of the unit disk D| onto itself, then it is generally true
for all z.sub.1, z.sub.2.epsilon.D|
f ( z 1 ) - f ( z 2 ) 1 - f ( z 1 ) * f ( z 2 ) .ltoreq. z 1 - z 2
1 - z 1 * z 2 , ( 39 ) ##EQU00034##
[0319] with equality for all z.sub.1, z.sub.2.epsilon.D|
specifically when f is an analytic automorphism of the unit disk
D|, and thus a Mobius transformation that isomorphically maps the
unit disk D| onto itself.
[0320] In the Poincare model of hyperbolic geometry, the Poincare
distance between two points z.sub.1, z.sub.2 on the unit disk is in
general measured as:
P ( z 1 , z 2 ) = arc tan h ( z 1 - z 2 1 - z 1 * z 2 ) . ( 40 )
##EQU00035##
[0321] The Schwarz-Pick theorem thus has the consequence that the
matching networks M.sub.1, M.sub.2, which are automorphisms of the
unit disk, preserve the Poincare distance.
[0322] Now, the matching networks M.sub.1, M.sub.2 that are
considered within the scope of the design of power amplifiers are
non-resistive, i.e., power preserving. Accordingly, such a matching
network M.sub.1, M.sub.2 does not transform any active point in the
Smith chart to a passive point or vice versa: The transforming
action of a non-resistive (and reciprocal) matching network
M.sub.1, M.sub.2 is an automorphism of the unit disk D|.
[0323] As is shown above, the following is also the case: A
matching network M.sub.1 that transforms a source impedance present
at an input A.sub.2 into a complex conjugate of a load impedance
exhibited at an output A.sub.1 of the matching network M.sub.1 when
traversed in a first direction, maps the load impedance onto the
complex conjugate of the source impedance when traversed in the
opposite direction. The same applies to the reflection factors on
account of the transforming action.
[0324] Lastly, together with the transforming action of a matching
network M.sub.1 traversed in a first direction, the transforming
action of the matching network M.sub.1 traversed in the opposite
direction is also always an automorphism of the unit disk D|.
[0325] To summarize, the following theorem thus applies: if
a) M is a non-resistive, reciprocal matching network M.sub.1, b)
f:D|.fwdarw.D| describes the transforming action of the matching
network M.sub.1 traversed in a first direction, c)
f.sup.R:D|.fwdarw.D| describes the transforming action of the
matching network M.sub.1 traversed in the opposite direction
(=reverted); d) and it is also true that f(a)=a' for two points a,
a'.epsilon.D|
[0326] then it follows that:
a. i) f.sup.R(a.sub.on'*)=a.sub.on* (41)
b. ii) P(a.sub.on,b.sub.on)=P(f(a.sub.on),f(b.sub.on)) (42)
c. iii)
P(a.sub.on'*,b.sub.on)=P(f.sup.R(a.sub.on'*),f.sup.R(b.sub.on))
(43)
[0327] wherein P(a.sub.on'*, b.sub.on) designates the Poincare
distance between the two points a.sub.on'* and b.sub.on (reflection
factors).
[0328] In FIG. 5, an exemplary embodiment for the relationship
expressed in the above theorem is illustrated graphically in the
form of a diagram, which is hereinafter referred to as the matching
constellation:
[0329] in an assumed forward direction from right to left, the
matching network M.sub.1 maps the load reflection factor a.sub.on
onto the transformed load reflection factor a.sub.on'. This
relationship is represented in FIG. 5 by the angled arrows labeled
with a.sub.on and a.sub.on'. The assumed forward direction V is
indicated by an arrow labeled with the formula symbol of the
describing function f.sub.aon,aon',.phi..
[0330] According to lemma i) of the above theorem, the reverted
matching network M.sub.1 maps the complex conjugate a.sub.on'* of
the transformed load reflection factor a.sub.on' onto the complex
conjugate a.sub.on* of the load reflection factor a.sub.on,
represented by the angled arrows labeled with a.sub.on'* and
a.sub.on*. The transformation direction R of the reverted matching
network M.sub.1 is indicated by an arrow labeled with the formula
symbol of the reverted describing function
f.sup.R.sub.aon,aon',.phi..
[0331] The matching network M.sub.1, traversed in the reverse
direction R, also maps the source reflection factor b.sub.on onto
the transformed source reflection factor b.sub.on', represented by
the angled arrows labeled with b.sub.on and b.sub.on'. The reverse
direction R is indicated by an arrow labeled with the formula
symbol of the reverted describing function
f.sup.R.sub.aon,aon',.phi..
[0332] Lemma i), applied to the describing function
f.sup.R.sub.aon,aon',.phi. of the matching network M.sub.1
traversed in the reverse direction, states that the complex
conjugate b.sub.on'* of the transformed source impedance b.sub.on'
is mapped onto the complex conjugate b.sub.on* of the source
impedance b.sub.on by the matching network M.sub.1 traversed in the
forward direction, indicated by the angled arrows labeled with
b.sub.on'* and b.sub.on*.
[0333] The statement of lemmas ii) and iii)--the preservation of
the Poincare distance under the describing function and under the
reverted describing function--is indicated in FIG. 5 by a pair of
ellipses for each: The preservation of the Poincare distance
between the complex conjugate a.sub.on'* of the transformed load
reflection factor a.sub.on' and the source reflection factor
b.sub.on under the reverted describing function
f.sup.R.sub.aon,aon',.phi. (lemma iii)) is shown schematically by a
first solid ellipse, which connects the angled arrows with
reference symbols a.sub.on'* and b.sub.on, and a second solid
ellipse, which connects the angled arrows with reference symbols
b.sub.on' and a.sub.on*.
[0334] The preservation of the Poincare distance between the
complex conjugate b.sub.on' of the transformed source reflection
factor b.sub.on' and the load reflection factor a.sub.on under the
describing function f.sub.aon,aon',.phi. (lemma ii)) is shown
schematically by a first dashed ellipse, which connects the angled
arrows with reference symbols a.sub.on and b.sub.on'*, and a second
dashed ellipse, which connects the angled arrows with reference
symbols a.sub.on' and b.sub.on*.
[0335] Furthermore, on account of the symmetry of the definition of
the Poincare distance under the operation of complex conjugation,
the Poincare distances between the complex conjugate a.sub.on'* of
the transformed load reflection factor a.sub.on' and the source
reflection factor b.sub.on, and between the complex conjugate
b.sub.on' of the transformed source reflection factor b.sub.on' and
the load reflection factor a.sub.on, which belong to the relevant
pairs of ellipses in FIG. 5, are equal.
[0336] If one maps a source reflection factor b.sub.on onto a
specific value of the transformed source reflection factor
b.sub.on', then in accordance with the matching constellation from
FIG. 5, the transformed load reflection factor a.sub.on' is
restricted to a Poincare circle about the complex conjugate
b.sub.on* of the source reflection factor b.sub.on. Here, a
Poincare radius is equal to the Poincare distance between the
complex conjugate a.sub.on* of the load reflection factor a.sub.on
and the determined value of the transformed source reflection
factor b.sub.on'.
[0337] A value is now sought from among the values of the
transformed load reflection factor a.sub.on' on the previously
defined circle for which a given parameter of the circuit--for
example a power gain--takes on an optimal value. The optimal value
of the parameter depends on the determined value of the transformed
source reflection factor b.sub.on'.
[0338] If one maps the load reflection factor a.sub.on (with the
aid of the matching network M.sub.1, now traversed in the opposite
direction) onto the optimal value for the transformed load
reflection factor a.sub.on', then, likewise in accordance with the
matching constellation from FIG. 5, the transformed source
reflection factor b.sub.on' lies on another Poincare circle of the
same radius, but about the complex conjugate a.sub.on* of the load
reflection factor a.sub.on. An optimum of the parameter can in turn
be found on the additional circle, now for the transformed source
reflection factor b.sub.on'. The optimum depends on the optimal
value, which for its part is defined with respect to the determined
value of the transformed source reflection factor b.sub.on'.
[0339] An iteration provides a pair having a specific value of the
transformed load reflection factor a.sub.on' and a specific value
of the transformed first source reflection factor b.sub.on', by
means of which the parameter of the circuit is optimized, under the
boundary condition of a given Poincare distance P.sub.R between the
complex conjugate a.sub.on* of the first load reflection factor
a.sub.on and the transformed first source reflection factor
b.sub.on'. This Poincare distance P.sub.R is equal to the Poincare
distance between the complex conjugate b.sub.on* of the source
reflection factor b.sub.on and the transformed load reflection
factor a.sub.on'.
[0340] In a simplified method for the exemplary embodiment from
FIG. 1, pairs that optimize the parameter of the circuit are
determined: Proceeding from a number of Poincare radii P.sub.R,
optimal reflection factor pairs on circles of the same Poincare
radius within two concentric families of Poincare circles about the
complex conjugate b.sub.on* of the first source reflection factor
b.sub.on and the complex conjugate a.sub.on* of the first load
reflection factor a.sub.on are found. This method is explained
below using FIG. 6 and FIG. 7.
[0341] FIG. 6 shows in a schematic Smith chart S:
[0342] a first load reflection factor a.sub.on,
[0343] a first source reflection factor b.sub.on,
[0344] the complex conjugate a.sub.on* of the first load reflection
factor a.sub.on,
[0345] the complex conjugate b.sub.on* of the first source
reflection factor b.sub.on,
[0346] a transformed first source reflection factor b.sub.on',
[0347] a transformed first load reflection factor a.sub.on',
[0348] the complex conjugate b.sub.on'* of the transformed first
source reflection factor b.sub.on',
[0349] the complex conjugate a.sub.on'* of the transformed first
load reflection factor a.sub.on',
[0350] another transformed source reflection factor b.sub.2'.
[0351] In addition to the reflection factors, FIG. 6 shows
[0352] a first Poincare circle K.sub.1 about the complex conjugate
b.sub.on* of the first source reflection factor b.sub.on,
[0353] a second Poincare circle K.sub.2 about the complex conjugate
a.sub.on* of the first load reflection factor a.sub.on,
[0354] the complex conjugate K.sub.1* of the first Poincare circle
K.sub.1,
[0355] an auxiliary Poincare circle H.sub.1 about the transformed
first source reflection factor b.sub.on',
[0356] the complex conjugate H.sub.1* of the auxiliary Poincare
circle H.sub.1, and
[0357] an additional auxiliary Poincare circle H.sub.2 about the
additional transformed source reflection factor b.sub.2'.
[0358] With the exception of the unit circle as the edge of the
Smith chart S, all circles shown in FIG. 6 have the same Poincare
radius, which Poincare radius is given as the Poincare distance
between the transformed first source reflection factor b.sub.on'
and the complex conjugate a.sub.on* of the first load reflection
factor a.sub.on, so that
[0359] the first load reflection factor a.sub.on lies on the
complex conjugate H.sub.1* of the auxiliary Poincare circle
H.sub.1,
[0360] the complex conjugate a.sub.on* of the first load reflection
factor a.sub.on lies on the auxiliary Poincare circle H.sub.1 and
on the additional auxiliary Poincare circle H.sub.2,
[0361] the transformed first load reflection factor a.sub.on' lies
on the first Poincare circle K.sub.1, and
[0362] the complex conjugate a.sub.on'* of the transformed first
load reflection factor a.sub.on' lies on the complex conjugate
K.sub.1* of the first Poincare circle K.sub.1.
[0363] A solid arrow indicates the mapping of the first source
reflection factor b.sub.on onto the transformed first source
reflection factor b.sub.on' by means of the matching network
M.sub.1, and a dashed arrow indicates the mapping of the complex
conjugate b.sub.on' of the transformed first source reflection
factor b.sub.on' onto the complex conjugate b.sub.on* of the first
source reflection factor b.sub.on by the reverted matching network
M.sub.1.
[0364] On account of the preservation of the Poincare distance
under the describing function f.sub.aon,aon',.phi. of the matching
network M.sub.1, during the mapping of the first source reflection
factor b.sub.on onto the transformed first source reflection factor
b.sub.on', the complex conjugate K.sub.1* of the first Poincare
circle K.sub.1 about the source reflection factor b.sub.on is
mapped onto the auxiliary Poincare circle H.sub.1 about the
transformed first source reflection factor b.sub.on'. In contrast,
if the first source reflection factor b.sub.on is transformed into
the additional transformed source reflection factor b.sub.2' by
means of the matching network M.sub.1, then the complex conjugate
K.sub.1* of the first Poincare circle K.sub.1 about the first
source reflection factor b.sub.on is mapped onto the additional
auxiliary Poincare circle H.sub.2 about the additional transformed
source reflection factor
[0365] At the same time, on account of the preservation of the
Poincare distance under the reverted describing function
f.sup.R.sub.aon,aon',.phi. of the matching network M.sub.1
traversed in the reverse direction, in the mapping of the complex
conjugate b.sub.on'* of the transformed first source reflection
factor b.sub.on' onto the complex conjugate b.sub.on* of the first
source reflection factor b.sub.on, the complex conjugate H.sub.1*
of the auxiliary Poincare circle H.sub.1 about the complex
conjugate b.sub.on'* of the transformed first source reflection
factor b.sub.on' is mapped onto the first Poincare circle K.sub.1
about the complex conjugate b.sub.on* of the first source
reflection factor b.sub.on.
[0366] Accordingly, for every value of the transformed first source
reflection factor b.sub.on', all possible values of the transformed
first load reflection factor a.sub.on' lie on the first Poincare
circle K.sub.1. For the transformed first source reflection factor
b.sub.on', a value of the transformed first load reflection factor
a.sub.on' on the first Poincare circle K.sub.1 is determined for
which the parameter of the circuit takes on a (local) optimum.
[0367] In addition, permissible values of the transformed first
load reflection factor a.sub.on' on the first Poincare circle
K.sub.1 are limited by the determination of the transformed
additional source reflection factor b.sub.2' on the second Poincare
circle K.sub.2 and (at the same Poincare distance from the complex
conjugate a.sub.on* of the first load reflection factor a.sub.on)
of the transformed first source reflection factor b.sub.on'.
[0368] For the additional transformed source reflection factor
b.sub.2', an additional value of the transformed first load
reflection factor a.sub.on' on the first Poincare circle K.sub.1 is
determined for which the parameter of the circuit takes on a
(local) optimum.
[0369] In a completely analogous manner, all values of the
transformed first source reflection factor b.sub.on' for which the
transformed first load reflection factor a.sub.on' is restricted to
the first Poincare circle K.sub.1 actually lie on the second
Poincare circle K.sub.2.
[0370] Accordingly, the determination of the pairs of a transformed
first source reflection factor b.sub.on' and a transformed first
load reflection factor a.sub.on' that optimize the parameter is
limited to pairs for which the Poincare distance of the transformed
first load reflection factor a.sub.on' from the complex conjugate
b.sub.on* of the first source reflection factor b.sub.on is equal
to the Poincare distance of the transformed first source reflection
factor b.sub.on' from the complex conjugate a.sub.on* of the first
load reflection factor a.sub.on.
[0371] This state of affairs is highlighted in a separate
illustration in FIG. 7. In a Smith chart S, FIG. 7 shows
[0372] the complex conjugate a.sub.on* of the first load reflection
factor a.sub.on,
[0373] the complex conjugate b.sub.on* of the first source
reflection factor b.sub.on,
[0374] a first family of points b.sub.s' of two transformed source
reflection factors,
[0375] a second family of points a.sub.s' of two transformed load
reflection factors, and
[0376] In addition to the reflection factors, FIG. 7 shows:
[0377] a first family of circles K.sub.1s of two first Poincare
circles about the complex conjugate b.sub.on* of the first source
reflection factor b.sub.on, which first family K.sub.1s contains a
Poincare circle with a first Poincare radius, and a Poincare circle
with a second Poincare radius, and
[0378] a second family of circles Kg.sub.s of second Poincare
circles about the complex conjugate a.sub.on* of the load
reflection factor a.sub.on, which second family K.sub.2s contains a
Poincare circle with the first Poincare radius and a Poincare
circle with the second Poincare radius.
[0379] Each transformed source reflection factor b.sub.s' from the
first family of points b.sub.s' lies on one Poincare circle from
the first family of circles K.sub.1s, and each transformed load
reflection factor a.sub.s' from the second family of points
a.sub.s' lies on one Poincare circle from the second family of
circles K.sub.2s.
[0380] For a set of given Poincare distances, pairs are formed,
each having one transformed first load reflection factor a.sub.on'
at a first Poincare distance from the complex conjugate b.sub.on*
of the first source reflection factor b.sub.on and one transformed
first source reflection factor b.sub.on' at the first Poincare
distance from the complex conjugate a.sub.on* of the first load
reflection factor a.sub.on, and one pair is determined among the
pairs of reflection factors thus determined such that the parameter
takes on an optimum.
[0381] Mobius transformations and the automorphisms of the unit
disk
[0382] A Mobius transformation is a mapping f of the complex number
plane onto itself, of the form:
f ( z ) = .alpha. z + .beta. .gamma. z + .delta. , ( 44 )
##EQU00036##
[0383] where z is a point on the complex number plane and .alpha.,
.beta., .gamma., .delta. are arbitrary complex constants.
[0384] While the group of Mobius transformations thus has six real
degrees of freedom (the fraction can be shortened by .delta., for
example, without changing the mapping, so that the four constants
and .alpha., .beta., .gamma., .delta. only represent three complex
degrees of freedom), the automorphism group of the unit disk is a
proper subgroup of the Mobius transformations: The automorphisms of
the unit disk can be represented as:
f ( z ) = .phi. z - z 0 1 - z 0 * z , .phi. = 1 ( 45 )
##EQU00037##
[0385] With a complex automorphism parameter z.sub.0 and a cyclic
degree of freedom .phi., the automorphism group, and thus the group
of transforming actions of non-resistive reciprocal matching
networks, have only three degrees of freedom (for a given
frequency).
[0386] If one requires a matching network M.sub.1 to transform a
first reflection factor a.sub.on into a second reflection factor
b.sub.on* different from the first,
f(a.sub.on)=b.sub.on*, (46)
[0387] where f describes the transforming action of the matching
network M.sub.1 traversed in the forward direction V, there remain
for the set N of transforming actions of all such matching networks
M.sub.1 only the cyclic degree of freedom .phi.: image and
counter-image of an arbitrary reflection factor among the set N are
closed curves.
[0388] The Schwarz-Pick theorem requires the form of Poincare
circles for the closed curves. Hence, the image N(a.sub.on') of a
third reflection factor a.sub.on' among the set N is a Poincare
circle about the second reflection factor b.sub.on* with a Poincare
radius equal to the Poincare distance P(a.sub.on, a.sub.on')
between the first reflection factor a.sub.on and the third
reflection factor a.sub.on'.
[0389] It follows, in particular, that one can choose the image
f(a.sub.on') of the third reflection factor a.sub.on' under the
transforming action f of the matching network M.sub.1 (for
reciprocal, power-preserving matching networks) only on a fixed
Poincare circle defined by the first and the second reflection
factors b.sub.on*. Furthermore, it follows that the transforming
action f of the matching network M.sub.1 is uniquely defined by the
choice of one such image f(a.sub.on') on the given Poincare
circle.
[0390] Lastly, if one solves the above representation of the
automorphisms for f(a.sub.on)=a.sub.on' for z.sub.0, one
obtains:
f ( z 1 ) = .PHI. z 1 - z 0 1 - z 0 * z 1 , f ( a on ) = a on ' (
47 ) z 0 = 1 - a on 2 a on 2 a on ' 2 - 1 a on ' - .PHI. - 1 - a on
' 2 a on 2 a on ' 2 - 1 a on ( 48 ) ##EQU00038##
[0391] This shows explicitly that the set of all describing
functions for non-resistive, reciprocal matching networks that map
a given load reflection factor a.sub.on onto a given transformed
load reflection factor a.sub.on' have only one real degree of
freedom.
[0392] The effects of the state of affairs described are
illustrated in FIG. 8. FIG. 8 shows, in the interior of the unit
circle 5, two families of circles inscribed inside one another. A
first family forms a family of concentric and equidistant circles
about the origin in the sense of the Euclidean metric of the
(Cartesian) plane. These circles are also concentric circles in the
framework of hyperbolic geometry of the plane and measured in
Poincare distance.
[0393] The second family of circles about a point differing from
the origin is equidistant and concentric in the Poincare sense, but
not when measured with the Euclidean metric of the plane.
[0394] FIG. 8 also shows two direction arrows, a first proceeding
from the origin, a second proceeding from the point differing from
the origin.
[0395] If the set of describing functions of all reciprocal,
non-resistive matching networks is limited to the subset F of the
functions that map the origin onto the point differing from the
origin, then the image of one of the circles from the first family
with a specific Poincare radius in the subset F is that circle from
the second family with the specific Poincare radius.
[0396] If, in addition to the origin and the point differing from
the origin into which the origin is transformed by means of the
matching network M.sub.1, a (single) additional pair is defined as
having a reflection factor on a Poincare circle (for a given
Poincare radius) about the origin, and its image under the matching
network M.sub.1 (if necessary, on a Poincare circle of the same
Poincare radius about the point differing from the origin), then
the transforming action of the matching network M.sub.1 in the
entire Smith chart is known, and the describing function is thus
uniquely defined.
[0397] The same applies when a second direction proceeding from the
image point is known in addition to a counter-image point and an
image point under the describing function of the matching network
M.sub.1 for a first direction proceeding from the counter-image
point.
[0398] The describing functions of reverted matching networks
[0399] A reverted matching network for a matching network M.sub.1
transforming a counter-image reflection factor m (e.g. m=a.sub.on)
into an image reflection factor n (e.g. n=a.sub.on') is described
by a reverted describing function
f.sup.R.sub.mn.phi.=f.sub.n*m*.phi.R (49)
[0400] with automorphism parameter z.sub.0.sup.R, where the equals
sign applies on account of symmetry. If one expresses the
describing function of the matching network M.sub.1 as
f ( z ) = .phi. z - z 0 1 - z 0 * z ( 50 ) with z 0 = 1 - m 2 m 2 n
2 - 1 n - .phi. 1 - n 2 m 2 n 2 - 1 m , ( 51 ) ##EQU00039##
[0401] it follows that
z.sub.0.sup.R=-e.sup.-i.phi..sup.Rz*.sub.0, (52)
[0402] and further:
{ f mn .phi. ( z 2 * ) = z 1 * = .phi. z 2 * - z 0 ( .phi. ) 1 - z
0 ( .phi. ) * z 2 * f mn .phi. R ( z 1 ) = f n * m * .phi. R ( z 1
) = z 2 = .phi. R z 1 - z 0 R ( .phi. R ) 1 - z 0 R ( .phi. R ) * z
1 } , ( 53 ) z 0 R = - - .phi. R z 0 * .fwdarw. z 1 * = .phi. -
.phi. R z 1 * , ( 54 ) ##EQU00040##
[0403] or
.phi.=.phi..sub.R,f.sup.R.sub.mn.phi.=f.sub.n*m*.phi. (55)
[0404] The describing function f of the matching network M.sub.1
traversed in the forward direction uniquely determines the
describing function f.sup.R of the reverted matching network; the
operation of reversion is mathematically well-defined.
[0405] The knowledge of the describing function f (and likewise of
the equivalent reverted describing function f.sup.R), the
application of which is used for designing matching networks that
optimize circuit properties, creates great freedom in determining
concrete matching networks whose transforming action physically
implements the describing function f at a given operating
frequency.
[0406] As has been shown, the transforming action of a
non-resistive, reciprocal matching network has three real degrees
of freedom at an operating frequency. If an image reflection factor
and a counter-image reflection factor (different from the image
reflection factor) associated with this image reflection factor
under the matching network M.sub.1 are defined, then only a single
real degree of freedom remains. In consequence, the image or
counter-image of every additional reflection factor under the
matching network M.sub.1 or the associated reverted matching
network is limited to a circle. Accordingly, if a second pair
having an image and a counter-image reflection factor--which can no
longer be freely chosen independently from one another--is defined,
the transformation properties of the matching network M.sub.1 are
largely known.
[0407] In the physical design of a matching network M.sub.1, the
unambiguous knowledge of the describing function f makes it
possible to freely choose which two pairs of image and
counter-image reflection factors are used for the determination,
and in which direction of passage which of the two counter-images
is transformed into its image.
[0408] While a uniquely determined describing function f belongs to
each matching network M.sub.1 at a fixed operating frequency, a
large class/set of an extremely wide variety of matching networks
and matching network topologies fit a given describing function f:
A describing function can be implemented in many ways in the form
of the matching network M.sub.1 whose transforming action is given
by the describing function f.
[0409] A physical matching network M.sub.1 is designed from given
transformation properties. For example, an adequately flexible
circuit topology for a matching network M.sub.1 is given. The
topology is converted into an equation with the component values as
variables. The equation is solved in accordance with the desired
transforming action.
[0410] Another method is to carry out a circuit optimization with a
circuit topology and variable component values with the aid of a
computer program for circuit simulation in order to implement the
desired transforming action with the aid of the circuit topology
used.
[0411] Furthermore, the describing function f additionally opens up
extensive possibilities in the investigation of parameters of a
circuit. In particular, all transformation properties of the
reciprocal, non-resistive matching network M.sub.1 characterized by
the describing function f at an operating frequency can be derived
exclusively from the describing function f--even before design or
knowledge of the matching network M.sub.1 itself.
[0412] An extremely important advantage and advancement is:
[0413] The method presented makes it possible from the outset, from
among all conceivable transforming actions of non-resistive,
reciprocal matching networks, to limit oneself to those that are
mathematically implementable in designing the circuit. The prior
trial-and-error method is no longer necessary.
[0414] Furthermore, the method presented here makes it possible to
take into account all effects of the transformation behavior on the
parameter of the circuit even without knowledge of a concrete
implementation of the transformation behavior defined by the
describing function f.
[0415] Hence, instead of having to determine the transformation
properties for a large number of previous, concrete matching
networks so as to be able to investigate their effect on the
circuit parameters, it is possible with the method described to
seek out, from among all mathematically possible transforming
actions, those through which the parameter of the circuit is
optimized. The subsequent implementation is limited to physical
matching networks with these few transformation properties.
[0416] The advance achieved by the method is explained below using
an especially simple exemplary application. In this context, the
amplifier chain as represented in FIG. 1 is used as a starting
point.
[0417] So that the impedance levels transform in a trivial manner
in a signal line occurring in a physical implementation of the
circuit, the matching network M.sub.1 is frequently designed in
such a manner that it has an impedance of 500 at its end facing the
signal line. To this end, a vector network analyzer is used, for
example. Using test connections of the network analyzer introduced
into the circuit, the mismatch from 50.OMEGA. of the connections of
the matching network M.sub.1 facing the signal line is
minimized.
[0418] In addition to the obvious task of this optimization method,
namely making the first and the second matching networks
independent from one another, the prior art already implicitly
accomplishes a second task: When non-resistive and reciprocal
matching networks are used, the amplifiers are terminated at their
connections with the complex conjugate of the relevant connection
impedance terminated, and thus the small-signal power gain of the
circuit is maximized.
[0419] Even without the above observations regarding the
Schwarz-Pick theorem, one can directly convince oneself of the
following using the symmetry properties of the transformation path
of the matching network M1 made up of lumped-constant reactive
elements in the Smith chart: Applied to an output impedance, the
matching network M1, traversed in the forward direction, results in
a target impedance. In contrast, with the reactive elements in
reverse order, the matching network M1 traversed in the reverse
direction maps the complex conjugate of the target impedance onto
the complex conjugate of the output impedance. The sequential
execution of the reversion of the matching network M1 and the
complex conjugation of the impedances results in a mirroring of the
transformation path on the real axis, including a change in the
direction of traversal.
[0420] If the output impedance is real, for example equal to 500,
freedom from reflections at the end of the matching network M1
distant from the amplifier thus results in complex conjugate
matching at its amplifier end. This matching is frequently designed
for maximum power gain.
[0421] If it is not the small-signal power gain that is to be
optimized, but instead, for example, the linear output power of an
amplifier stage under the boundary condition of a given maximum
mismatch between a 50.OMEGA. load and the impedance seen into the
output of the matching network M1 distant from the amplifier, one
has heretofore been largely dependent on trial and error: Until
now, the matching network has been experimentally altered following
the reflection-free design of the matching network at its output
side until the required boundary conditions were met.
[0422] In so doing, the new method avoids the need to use costly
and space-consuming non-reciprocal circuit elements in order to be
able to access the transforming actions of the matching network
independently in the direction of signal flow and in the opposite
direction as well.
[0423] Another application of the method is the use and evaluation
of load pull data in the determination of the parameter of the
circuit as part of the development of matching networks: When
applied with a real load reflection factor a.sub.on, the method
makes it possible to determine the output-side mismatch as a
function of the transformed load reflection factor a.sub.on' for
every given transformed load reflection factor a.sub.on'.
[0424] Using the method it is possible, in particular for the case
of a vanishingly small load reflection factor a.sub.on, to specify
a family of circles as loci of the transformed load reflection
factors a.sub.on' that result in a given output-side mismatch when
non-resistive, reciprocal matching networks are used. In this way,
expanded possibilities are opened up for the use of load pull data
in circuit design.
[0425] As follows from the preservation of the Poincare distance,
the transforming action of non-resistive, reciprocal matching
networks is uniquely determined by specifying two pairs of one
image factor and one counter-image reflection factor each. The two
image reflection factors used to define the transformation
properties can be located on the same side of the matching
network.
[0426] As has been shown, mathematically specifying the
transforming action of a non-resistive, reciprocal matching network
M.sub.1, for example using a describing function f, is equivalent
to specifying the transforming action of the associated reverted
matching network, for example using the reverted describing
function f.sup.R.
[0427] This can be used to go from the specification of the
transformation properties using two image reflection factors on the
same side of the matching network to a specification of the
transformation properties using two image reflection factors on
different sides of the matching network and vice versa.
[0428] It must always be kept in mind that identifiers containing
terms such as "load" do not permit any implication as to the
location of the quantities identified thereby relative to the
matching network M.sub.1 and measured with reference to the
direction of the signal flow within the circuit. Hence, the
situation is also encompassed in which, for example, the circuit
element identified as the "variable load" can also be considered a
source in electrical engineering terms.
[0429] In the other embodiment, the transformation of the two
counter-image impedances takes place with passage through the
matching network in the same direction. This is shown, for example,
in FIG. 9 using a circuit by way of example.
[0430] In a method for designing this electronic circuit in the
exemplary embodiment for FIG. 9, a second parameter G.sub.2 of the
circuit is to be optimized. The circuit has a second matching
network M.sub.2 with a third connection A.sub.3 and a fourth
connection A.sub.4. The circuit has, connected to the third
connection A.sub.3, a variable load L with a first operating state
off and a second operating state on. In accordance with the second
and third load reflection factors c.sub.off, c.sub.on, the
impedance of the load L is also different in the two operating
states.
[0431] Matching in the Case of Parallel Circuit of Multiple Circuit
Elements
[0432] What is important in the exemplary embodiment below is,
firstly, to determine the transforming actions for the
mathematically permissible, non-resistive reciprocal matching
networks, using these transforming actions to ascertain the effect
on parameters of the circuits, and only once an optimal
transforming action has been found, to design a matching network or
modify an existing matching network, for example for designing the
matching networks of load-modulation amplifiers, in particular for
the parallel circuit of two circuit elements (amplifiers).
[0433] For the type of load-modulation amplifier that is doubtless
the most well-known in the technical field, the Doherty amplifier,
the designation "peak branch" can be used for the path having a
first source element Q.sub.1 and a first matching network M.sub.1,
and the designation "main branch" can be used for the path having a
second source element Q.sub.2 and second matching network
M.sub.2.
[0434] In the interest of better understanding, the method for
designing matching networks M.sub.1, M.sub.2 is explained below
with particular reference to the special case of the Doherty
amplifier. This is in no way intended to imply that the application
of the method is limited to the circuit topology of the Doherty
amplifier.
[0435] In order to emphasize that the method extends far beyond an
application for the Doherty amplifier, the following exemplary
application is explained:
[0436] Using the detail illustrations in FIG. 12 ff., the
nomenclature will be clarified first and an introduction to the
method of operation of a load-modulation amplifier will be
presented.
[0437] FIG. 12 applies to a circuit topology of a load-modulation
amplifier. For the application of the load-modulation amplifier,
FIG. 12 shows, specifically:
[0438] a main amplifier Q.sub.2 with a second (main) source
reflection factor d.sub.on,
[0439] a peak amplifier Q.sub.1 with a first (peak) source
reflection factor b.sub.off at a low input signal level and a third
(peak) source reflection factor b.sub.on at a high input signal
level,
[0440] a T-section T with a first connection E.sub.1 as first
input, a second connection E.sub.2 as second input, and a third
connection E.sub.3 as output, wherein a load L with the load
impedance Z.sub.L is connected to the third connection E.sub.3 of
the output,
[0441] a first matching network M.sub.1, which can also be
designated as the peak matching network, with a first connection
A.sub.1 and a second connection A.sub.2, wherein the first
connection A.sub.1 is connected to the first connection E.sub.1 of
the T-section T and wherein the second connection A.sub.2 is
connected to the peak amplifier Q.sub.1 as first source element,
and
[0442] a second matching network M.sub.2, which can also be
designated as the main matching network M.sub.2, with a third
connection A.sub.3 and a fourth connection A.sub.4, wherein the
third connection A.sub.3 is connected to the second connection
E.sub.2 of the T-section T and wherein the fourth connection
A.sub.4 is connected to the main amplifier Q.sub.2.
[0443] In FIG. 12 ff., the aforementioned reflection factors are
labeled with the corresponding reference symbols.
[0444] For ease of understanding, FIGS. 17, 18, 19 show equivalent
circuits for a symmetrically driven T-section T in three detail
illustrations. FIG. 17 shows a star circuit having a load impedance
Z.sub.L and two identical source impedances Z. FIG. 18 shows a
circuit equivalent hereto, by means of which the symmetry
properties can be worked out more easily: The load impedance
Z.sub.L has been replaced by a parallel circuit of two identical
impedances with values 2Z.sub.L twice that of the load impedance
Z.sub.L. When identical signals are applied to the connections of
the source impedances Z that are distant from the load impedance
Z.sub.L, all relationships in the circuit become fully symmetrical.
Maxwell's equations require a so-called magnetic wall M, as a
result of which the circuit is virtually divided into two circuit
sections, each of which includes a source impedance Z and a doubled
load impedance 2Z.sub.L in series connection. This situation is
shown in FIG. 19.
[0445] Accordingly, if one of the two source impedances Z in FIG.
17 were replaced by an open circuit, the second source element
Q.sub.2 would "see" only the single load impedance Z.sub.L.
However, if both source elements Q.sub.1, Q.sub.2 output an
identical signal, then the source elements Q.sub.1, Q.sub.2 share
the admittance of the load impedance Z.sub.L equally, so that both
source elements Q.sub.1, Q.sub.2 with the source impedance Z
experience the doubled load impedance 2Z.sub.L, in accordance with
FIG. 19.
[0446] In a Doherty amplifier, the peak branch is typically
operated in class C. Thus, the peak branch is limited at low input
signal levels. In a design of the first (peak) matching network
M.sub.2 suitable for this purpose, this matching network provides
an open circuit at the first connection A.sub.1 as the first
transformed (peak) source reflection factor b.sub.off' in a first
operating state off; the main amplifier branch depends solely on
the admittance of the load impedance Z.sub.L.
[0447] In contrast, at high input signal levels in a second
operating state on, the peak amplifier branch is dynamically driven
on. It adds a signal, which is similar to the signal generated by
the main amplifier branch at the second connection E.sub.2 of the
T-section T, at the first connection E.sub.1 of the T-section T.
The two amplifier branches share the admittance of the load
impedance Z.sub.L: Because of the dynamic driving-on of the peak
amplifier branch operated in class C, the (second/third) (main)
load reflection factor c.sub.off, c.sub.on acting for the main
amplifier branch, and thus the (second/third) transformed (main)
load reflection factor c.sub.off', c.sub.on', is modulated.
[0448] An intermediate result and the conclusions to be derived
from the two intermediate results are explained below using FIG.
15.
[0449] Specifically, FIG. 15 shows:
[0450] the edge .delta. of the unit circle in the reflection factor
plane,
[0451] the geometric locus K.sub.1' of all reflection factors that
are determined by the parallel circuit of the load impedance
Z.sub.L with one relevant additional impedance, wherein each
additional impedance is associated with a reflection factor on the
first Poincare circle K.sub.1 in accordance with FIG. 13; reference
is made to FIG. 18 concerning the load impedance Z.sub.L and
doubled load impedance 2Z.sub.L,
[0452] the reflection factor c.sub.on that is associated with the
doubled load impedance 2Z.sub.L,
[0453] drawn in thin lines and with no reference symbol, a
concentric, in the Poincare sense, family of Poincare circles about
the reflection factor c.sub.on that is associated with the doubled
load impedance 2Z.sub.L,
[0454] highlighted with bold lines, a third Poincare circle K.sub.3
from the family of Poincare circles, and
[0455] two points of intersection c.sub.off,1, c.sub.off,2 between
the third Poincare circle K.sub.3, highlighted with bold lines,
from the family of Poincare circles and the geometric locus
K.sub.1', as explained above.
[0456] According to the first intermediate result, all permissible
values y' for the first load reflection factor a.sub.on lie on the
geometric locus K.sub.1' in accordance with FIG. 13, and moreover,
lie on the third Poincare circle K.sub.3 in accordance with the
second intermediate result.
[0457] When a transformed first (peak) load reflection factor
a.sub.on' that is sought for the area of application of the peak
amplifier Q.sub.1 in FIG. 12 is known, this knowledge in
combination with the load impedance Z.sub.L defines the geometric
locus K.sub.1'.
[0458] When the desired transformed second and third (main) load
reflection factors c.sub.off', c.sub.on' for the desired area of
application of the main amplifier Q.sub.1 are known, this knowledge
in combination with the value of the load impedance Z.sub.L also
defines the third Poincare circle K.sub.3.
[0459] Only the two points of intersection c.sub.off,1, c.sub.off,2
of the defined geometric locus K.sub.1' and the defined third
Poincare circle K.sub.3 result as permissible values for the second
(main) load reflection factor c.sub.off.
[0460] For example, the parameter of the circuit is a sum of
squares of a first and second geometric distance. Here, the first
geometric distance is defined between an arbitrary reflection
factor and the third Poincare circle K.sub.3. In contrast, the
second geometric distance is defined between the arbitrary
reflection factor and the geometric locus K.sub.1'. By this means,
the second (main) load reflection factor c.sub.off is largely
defined. As a result, the first cyclic degree of freedom associated
with the main amplifier branch and the second cyclic degree of
freedom associated with the peak amplifier branch, and consequently
the complete describing functions of both matching networks
M.sub.1, M.sub.2, are largely determined as well.
[0461] In addition to the limitations on possible value pairs
having a transformed second (main) load reflection factor
c.sub.off' and a transformed third (main) load reflection factor
c.sub.on' resulting from the circumstances explained, the
near-complete definition of the describing functions is explained
in detail with the aid of FIG. 16.
[0462] FIG. 16 shows:
[0463] the edge .delta. of the unit circle in the reflection factor
plane,
[0464] a third value c.sub.on'.sub.opt of a transformed third
(main) load reflection factor c.sub.on',
[0465] drawn in thin lines and with no reference symbol, a first
family of (in the Poincare sense) concentric Poincare circles about
the third value c.sub.on'.sub.opt, spanning an annular region in
the interior of the unit circle,
[0466] also drawn in thin lines, a second family of circles, each
of which touches the inner and outer edges of the annular
region,
[0467] a second value c.sub.off'.sub.opt of a transformed second
(main) load reflection factor c.sub.off',
[0468] highlighted with bold lines, one circle K.sub..phi.p from
the first family and one circle K.sub..phi.m from the second
family, wherein the highlighted circles intersect at the second
value c.sub.off'.sub.opt.
[0469] The development of a load-modulation amplifier of the
Doherty type starts with determining the effect of the values of
the transformed load reflection factors on the main and peak
amplifiers to be used. To this end, load pull measurements of
quantities such as the curve of large-signal power gain with output
power are performed. From the load pull measurements, it is
possible to measure a compression behavior or an efficiency of the
power gain at a given compression, for example, as a function of
load reflection factor. Using these measurements, an optimal load
under full drive can be defined, for example as a load by which a
compression power is optimized at an operating frequency.
Similarly, a target impedance that is to be used as a goal for the
main amplifier under moderate input levels can be obtained from the
measurement. This is, for example, a load by which an efficiency of
the power gain at a given fraction of the maximum compression power
is maximized at the given operating frequency. In the method for
designing the matching networks in a Doherty amplifier, the goal in
a first method step is to achieve the result in both amplifier
paths that twice the (real) load impedance is transformed into the
optimal load under full drive. In another step, by inserting a line
of appropriate length with a line impedance equal to the load
impedance between the peak matching network and the T-section, the
transformed peak source impedance under low input signal levels is
therefore turned into an open circuit to the extent possible. By
this means, the losses that the signal of the main amplifier path
experiences at the T-section are minimized. In this process, a part
of the signal power into the output of the peak amplifier branch is
lost. If one limits oneself to non-resistive, reciprocal matching
networks in both the main and the peak amplifier branches, then
each of the two has three degrees of freedom.
[0470] Using FIG. 12 to FIG. 15, the result for the prevalent case
of real load impedances Z.sub.L of the load L is that the smallest
possible circle from the family of concentric circles in FIG. 15 is
sought, wherein the smallest possible circle (K.sub.3) intersects
the geometric locus K.sub.1'. In this process, the Poincare radius
of the concentric circles in FIG. 15 is given by the third Poincare
distance P.sub.3 between the transformed second and third (main)
load reflection factors c.sub.off', c.sub.on'.
[0471] In comparison to prior methods for designing load-modulation
amplifiers in which the signal losses are minimized at low input
levels, the advantage is obtained by means of the exemplary
embodiment in FIGS. 12 to 16 that the achievable swing is not
minimized at the same time.
[0472] A third Poincare distance P.sub.3 established between the
transformed second and third (main) load reflection factors
c.sub.off', c.sub.on' has--as explained above--the consequence of a
defined set of possible values for the cyclic degree of freedom
associated with the peak amplifier branch. The concentric circles
in FIG. 16 each correspond to a fixed Poincare distance between the
transformed second and third (main) load reflection factors
c.sub.off', c.sub.on' and hence correspond to a fixed value of the
cyclic degree of freedom associated with the peak amplifier
branch.
[0473] Accordingly, for a defined value of the third transformed
(main) load reflection factor c.sub.on', and hence two exhausted
degrees of freedom for the second (main) matching network M.sub.1,
the location of the possible values for the transformed second
(main) load reflection factor c.sub.off' on a fixed circle among
the concentric circles in FIG. 15, and thus a defined cyclic degree
of freedom associated with the peak amplifier branch, is determined
by the single cyclic degree of freedom associated with the main
amplifier branch that remains in the matching system: Along the
concentric circles, the cyclic degree of freedom associated with
the peak amplifier branch is fixed in each case, and the cyclic
degree of freedom associated with the main amplifier branch is
variable.
[0474] The reverse applies for the second family of circles: Each
of these corresponds to a fixed value of the cyclic degree of
freedom associated with the main amplifier branch, while a locus
along one of the circles of the second family is parameterized by
the variable cyclic degree of freedom associated with the peak
amplifier branch.
[0475] As compared to an experimental optimization, the present
exemplary embodiment has the advantage of using all degrees of
freedom.
[0476] In the present exemplary embodiment, optimal load impedances
for the two operating cases (high and low input signal levels) are
determined at the outset using load pull measurements. For a
simpler explanation, but without limiting the method according to
the invention hereto, the starting assumption in the following is
that in designing the main and peak matching networks M.sub.2,
M.sub.1 using the method from the exemplary embodiment, the values
of the transformed load reflection factors at high input signal
levels for a maximum peak power are likewise determined at the
outset. In this process, the two cyclic degrees of freedom
remain.
[0477] In the present exemplary embodiment from FIG. 16, both
cyclic degrees of freedom are used so as to be able to freely
determine the transformed second (main) load reflection factor
c.sub.off' in the region spanned by the concentric circle family in
FIG. 16. For example, the second (main) load reflection factor
c.sub.off is determined in order to optimize an efficiency at a
desired fraction of the maximum output power. This achieves the
advantage that the efficiency increase achieved under low input
signal levels far outweighs a reduction in efficiency resulting
from additional losses due to a tolerated further deviation of the
transformed first (peak) source reflection factor b.sub.off' from
an open circuit.
[0478] Furthermore, an additional advantage is achieved by the
method in the present exemplary embodiment: With the aid of the
method, for any desired triplet of
[0479] a transformed second (main) load reflection factor
c.sub.off',
[0480] a transformed third (main) load reflection factor c.sub.on',
and
[0481] a transformed first (peak) load reflection factor
a.sub.on',
[0482] the complete transformation properties of the main and peak
matching networks M.sub.2, M.sub.1 can be determined even before
the knowledge of a physical implementation of these transformation
properties in a concrete circuit.
[0483] Using the first and third (peak) source reflection factors
b.sub.off, b.sub.on accessible to measurement, as well as a second
(main) source reflection factor d.sub.on that can also be
ascertained by measurement methods, the impedance level at the
T-section T, and hence the combination losses, can be ascertained
computationally under both operating conditions when the describing
functions of the (peak and main) matching networks M.sub.1, M.sub.2
are known.
[0484] Proceeding from load pull measurements of the electrical
characteristics of the peak and the main amplifiers Q.sub.1,
Q.sub.2, the method of the present exemplary embodiment accordingly
makes it possible to determine the electrical characteristics--for
example, gain and efficiency as a function of the output power--for
a load-modulation amplifier made up of the peak and the main
amplifiers Q.sub.1, Q.sub.2 as a function of the aforementioned
arbitrary triplet of reflection factors.
[0485] Thus it is possible, even without specifying concrete
implementations of the matching networks M.sub.1, M.sub.2, to first
optimize the characteristics of the load-modulation amplifiers
using the describing functions of the matching networks M.sub.1,
M.sub.2. Only after a best possible pair of describing functions
has been found does the design of the associated ideal pair of
matching networks M.sub.1, M.sub.2 take place. The method is fully
automated in this regard, for example based on an automatic load
pull measurement system.
[0486] The limitation of the description using the explanatory
figures to the symmetrical case serves only to simplify the
description. The validity and applicability of the exemplary
embodiments of the method for designing asymmetrical
load-modulation amplifiers remains unaffected thereby. For example,
the method of the exemplary embodiments is directly applicable to
load-modulation amplifiers with unequal division ratios. It is also
possible to apply the described exemplary embodiments to multipath
load-modulation amplifiers.
[0487] A further exemplary embodiment of a method for designing
matching networks for low-loss power addition is provided using
FIG. 22. In a T-section T provided as a summing element, a first
source element Q.sub.1 with a first source reflection factor b is
connected to a first connection E.sub.1 of a T-section T through a
first matching network M.sub.1. A second source element Q.sub.2
with a second source reflection factor d is connected to a second
connection E.sub.2 of the T-section T through a second matching
network M.sub.2. A load L with a load impedance is connected to a
third connection E.sub.3 of the T-section T.
[0488] In the case of identical source reflection factors b, d and
excitation of the inputs of a T-section T with identical phase and
power, the two inputs are isolated from one another by symmetry.
Moreover, if the source impedances are equal to twice the load
impedance of the load L, the power addition is reflection-free and
lossless.
[0489] Continuing the above remarks, for a real load impedance
Z.sub.L an identity of the source impedances and twice the load
impedance is present precisely when two amplifier branches operated
at the point of maximum small-signal power gain are used as
sources.
[0490] For the lossless addition of, e.g., the output signals of
two amplifier branches that are identical but are operated at their
respective optimum powers, the most independent access to the
transforming action of a matching network M.sub.1, M.sub.2 in the
direction of the signal flow (forward direction V), and opposite to
the signal flow (reverse direction R), is desirable. In this
context, independent access means that the two matching networks
M.sub.1, M.sub.2 are allowed to transform differently.
[0491] An additional, advantageous exemplary embodiment, which is
explained below with reference to FIG. 22, permits access of this
type that is independent to the greatest possible extent, and thus
permits a design method for designing the matching networks
M.sub.1, M.sub.2 of two parallel amplifier branches that are to be
joined through a T-section T.
[0492] In a concrete possible application case for the method, the
following are assumed:
[0493] a first power amplifier as first source element Q.sub.1,
[0494] a second power amplifier as second source element
Q.sub.2,
[0495] a first transformed load reflection factor a', and
[0496] a second transformed load reflection factor c'.
[0497] The first value a'.sub.opt here is a target value for the
first transformed load reflection factor a'. It can be determined,
for example at the start of the design of the circuit, in that
measurements are performed at the first source element Q.sub.1 at a
load pull measurement station. For example, a desirable value for
the first transformed load reflection factor a', which is set as
the first value a'.sub.opt and which optimizes an efficiency of a
power gain of the first source element Q.sub.1, is determined at a
compression of the power gain over the output power of one
decibel.
[0498] For example, the second value c'.sub.opt is determined as
the target value of the second transformed load reflection factor
c' using measurements at the second source element Q.sub.2.
[0499] For the case that the first value a'.sub.opt differs from
the complex conjugate b* of the first source reflection factor b
(consequently, the first source element Q.sub.1 is not to be
operated at the maximum of its small-signal power gain), a
reflection loss is produced for a signal output from the first
source element Q.sub.1 at the transition from the first matching
network M.sub.1 to the T-section T.
[0500] If the first and second source elements Q.sub.1, Q.sub.2 are
not isolated from one another in the design of the first and the
second matching networks M.sub.1, M.sub.2, then the signal output
from the first source element Q.sub.1 that is transmitted to the
load L is attenuated in that a part of the signal power is lost in
the second output. In designing the matching networks M.sub.1,
M.sub.2 according to the exemplary embodiment described, these
losses are minimized, while in addition there is only a slight
deviation from the values a'.sub.opt, c'.sub.opt that optimize the
source characteristics.
[0501] Only through the present exemplary embodiment of determining
the reflection factors "seen" into the output of a matching network
M.sub.1, M.sub.2 in a manner on a Poincare circle, is it possible
to arrive at matching networks M.sub.1, M.sub.2 by design means. In
this process, the losses are minimized by means of the matching
networks M.sub.1; M.sub.2, while at the same time there is only a
slight deviation from the reflection factor values a'.sub.opt,
c'.sub.opt that optimize the source characteristics.
[0502] With regard to the greatest possible simplicity of
representation, the derivation is explained using a real input
impedance of the load, without thereby limiting the method to real
load impedances. For example, the (not necessarily real) load
impedance is determined as the reference impedance of the
reflection factors. In this case, it is generally advantageous to
choose the quotient using the difference between an impedance and
the reference impedance as the dividend, and the sum of the
impedance and the complex conjugate of the reference impedance as
the divisor. The reflection factor for the (not necessarily real)
load impedance is real, so in the representation of the impedances
of images with finite imaginary parts we can change over to
individual reflection factors with vanishing imaginary parts.
[0503] One obtains a lossless power addition when the first source
amplifier as the first source element Q.sub.1 and the first
matching network M.sub.1, as well as the second source amplifier as
the second source element Q.sub.2 and the second matching network
M.sub.2, produce signals of equal phase and identical amplitude at
the first and second inputs of the T-section T with application of
appropriate signals, and the transformed first output impedance of
the first source element Q.sub.1 is equal to the transformed second
output impedance of the second source element Q.sub.2, which is
equal to the doubled load impedance.
[0504] Freedom from reflections between the first output impedance
of the first matching network M.sub.1 and the input impedance
measured into the first input of the T-section T prevails precisely
when the first source amplifier Q.sub.1 is operated at the maximum
of its small-signal power gain on the output side.
[0505] In exactly the same way, freedom from reflections between
the second output impedance of the second matching network M.sub.2
and the input impedance measured into the second input of the
T-section T prevails precisely when the second source amplifier
Q.sub.2 is operated at the maximum of its small-signal power gain
on the output side.
[0506] In accordance with the foregoing, lossless power addition
according to the prior art requires operation of the first and of
the second source amplifiers at the respective maxima of their
small-signal power gains.
[0507] Investigations by the applicant have shown that a first
sinusoidal signal at a first signal level from a first source
amplifier Q.sub.1 and a second sinusoidal signal of the first
signal level from a second source amplifier Q.sub.2 can be
losslessly superposed at a reciprocal T-section T with a suitable
choice of the relative phase of the first and second sinusoidal
signals precisely when
[0508] the source conductances 1/Z1, 1/Z2 are first equal to half
the load conductance 1/Z.sub.L,
Re ( 1 Z 1 ) = Re ( 1 Z 2 ) = Re ( 1 2 Z L ) , ( 56 )
##EQU00041##
[0509] while at the same time the imaginary parts of the
admittances cancel out in the sum:
Im ( 1 Z 1 ) = - Im ( 1 Z 2 ) . ( 57 ) ##EQU00042##
[0510] In both equations, Z.sub.1 represents one source impedance
experienced at the T-section, Z.sub.2 represents the other source
impedance experienced at the T-section, and Z.sub.L stands for the
load impedance. In particular, Z.sub.1 and Z.sub.2 are complex
conjugates of one another. In the borderline case of vanishingly
small imaginary parts of sources and loads, the two formulas
specialize on the solution for the impedances in accordance with
the previous prior art. To be geometrically illustrative, the
formulas mean that the two source impedances Z.sub.1, Z.sub.2 lie
on a common conductance circle with the doubled load impedance.
[0511] For the given values of the source conductances 1/Z.sub.1,
1/Z.sub.2 and for an appropriate phase position of the two signals
relative to one another, the input reflection factor of each input
of the T-section T shifts to the value of the transformed source
reflection factor as a result of load modulation by the signal of
the other respective source branch: For lossless addition of the
source signals in the T-section T, the part of the signal output
from the first source element that is reflected back at the first
input of the T-section T and the part of the signal output from the
second source element Q.sub.2 flowing through the first input of
the T-section T into the first signal path cancel each another out.
The total power output from both source elements Q.sub.1, Q.sub.2
is delivered to the load L. Hence, the two source elements Q.sub.1,
Q.sub.2 preferably are operated at the maximum of their
small-signal power gain to start with.
[0512] The first transformed source reflection factor b' and the
second transformed source reflection factor d' have significantly
different values, however. This characteristic is preserved when
one continuously departs from complex conjugate matching at the
output of the source elements Q.sub.1, Q.sub.2. For example,
termination conditions at the output side are specified that
optimize a source efficiency.
[0513] Due to the non-vanishing imaginary part of the transformed
source reflection factors b', d' and the broken symmetry of the
circuit including the T-section T, the first load reflection factor
a also differs significantly from the reflection factor associated
with the doubled load impedance 2Z.sub.L, just as it differs from
the second load reflection factor c.
[0514] For the exemplary embodiment from FIG. 22, a new pair of
slightly changed load reflection factors a'.sub.est, c'.sub.est
that differs only slightly from the known pair and is compatible
with the mathematical limitations on the transforming action of
non-resistive reciprocal matching networks M.sub.1, M.sub.2 is
first determined from the source reflection factors b, d and the
known pair of ascertained transformed load reflection factors a',
c'. The new pair of varied load reflection factors a'.sub.est,
c'.sub.est permits a largely lossless power addition at the
T-section T for a suitable choice of the relative phase positions
of the superposed signals from the two source elements Q.sub.1,
Q.sub.2.
[0515] For example, if the first matching network M.sub.1 maps the
first load reflection factor a onto the first value a'.sub.est
(which optimizes the characteristics of the first source element
Q.sub.1), then the transformed first load reflection factor a' lies
on a Poincare circle about the complex conjugate b* of the first
source reflection factor b. The same applies for the transformed
second load reflection factor c'.
[0516] The goal is the most lossless power addition attainable. A
prerequisite for this is that the transformed first and second
source reflection factors b', d' are complex conjugates of one
another. A further prerequisite is that both have the same Poincare
distance from the reflection factor that corresponds to the complex
conjugate 2Z.sub.L* of the doubled load impedance 2Z.sub.L, wherein
the first and second reflection factors are equal.
[0517] Because of the general characteristics of non-resistive,
reciprocal matching networks shown in FIG. 5, this absolutely
requires the third distance P.sub.3--which is to say the Poincare
distance of the transformed first load reflection factor a' from
the complex conjugate b* of the first source reflection factor
b1--and the equal fourth distance P.sub.4--which is to say the
Poincare distance of the transformed second load reflection factor
c' from the complex conjugate b* of the second source reflection
factor b.
[0518] In order to achieve the least possible difference of the
transformed load reflection factors a', c' from the reflection
factors that optimize the source characteristics, and at the same
time to preserve largely lossless power addition at the T-section
T, one must depend on a technical compromise:
[0519] In FIG. 23, the case where the third distance P.sub.3 is
equal to the fourth distance P.sub.4 has been chosen for the
illustration. For this value of the third and fourth distances
P.sub.3, P.sub.4, a minimum distance results between the first
value a'.sub.opt and the third value a'.sub.est, for example, when
the transformed first load reflection factor a' is determined at a
first value a'.sub.opt and the complex conjugate b* of the first
source reflection factor b is determined at a first distance
P.sub.1 from the first value a'.sub.opt. The same applies to the
determination of the transformed second load reflection factor c'
and of the second value c'.sub.opt.
[0520] The distance value P.sub.aus, the first value a'.sub.opt of
the transformed first load reflection factor a', and the second
value c'.sub.opt of the transformed second load reflection factor
c' are determined by variation of the third distance and the equal
fourth distance, P.sub.3, P.sub.4. The determination of the first
value and of the second value is carried out in that the geometric
mean of the first and the second distances P.sub.1, P.sub.2 is
minimized.
[0521] As explained above, by means of the additional method steps
the losses are minimized while at the same time the minimum
possible difference from the first value a'.sub.opt and second
value c'.sub.opt is achieved.
[0522] For the exemplary embodiments for the method for designing
matching networks, the essential steps can be summarized as
follows:
[0523] Carrying out an estimate for a function describing the
transforming action of the matching network M.sub.1, M.sub.2 as an
isomorphism of the unit disk in the reflection factor plane,
[0524] Utilizing the invariance of the Poincare distance of two
reflection factors under the matching networks M.sub.1, M.sub.2
encompassed by this estimate for defining a transforming action
optimizing the circuit parameters,
[0525] Determining a matching network M.sub.1, M.sub.2, that
exhibits a transforming action optimizing the circuit
parameters.
[0526] In electrical engineering terms, the first point reflects a
limitation to non-resistive, reciprocal matching networks M.sub.1,
M.sub.2.
[0527] The transforming action of non-reciprocal matching networks
M.sub.1, M.sub.2 can have a finite defect, which is to say that it
can map a non-trivial subspace of the reflection factor plane to
zero. In this case, it is at most an isomorphism of a subspace of
the reflection factor plane, but not of the unit circle. An example
thereof is the mapping matrix describing the transforming action of
a two-pole isolator, a 2.times.2 matrix with a one on the first
main diagonal element and zeroes in the other three locations.
[0528] In contrast, resistive matching networks map individual
reflection factors with a magnitude greater than one ("active
points") into the unit disk ("passive points"). Therefore, the
transforming action of resistive matching networks can still be
bijective, but in general is not an isomorphism of the unit
disk.
[0529] However, because of the Schwarz-Pick theorem, it is the case
for all automorphisms of the complex unit disk that they preserve
the Poincare distance. As has been shown using multiple examples,
this invariance can be employed advantageously to determine
transformation properties of matching networks M.sub.1, M.sub.2
through which circuit parameters are optimized insofar as the
circuit parameters depend on the transformation of more than one
reflection factor by the matching network M.sub.1, M.sub.2.
[0530] Lastly, the use of the method of the exemplary embodiments
automatically determines only those circuit-parameter-optimizing
transforming actions that leave the Poincare distances of two
points invariant, so that the optimization extends only to
transforming actions that can be implemented by non-resistive,
reciprocal matching networks M.sub.1, M.sub.2. In the third point
of the method, a matching network M.sub.1, M.sub.2 of this type is
specified that is characterized by the desired transformation
properties.
[0531] Accordingly, the matching networks obtained can be
characterized in that using the invariance of the Poincare distance
of two reflection factors, circuit parameters that depend on the
transformation of more than one of the reflection factors by the
matching network M.sub.1, M.sub.2 are optimized.
[0532] In contrast to conventional load-modulation amplifiers of
the Doherty type, the layouts of the matching networks achieved are
much smaller. This is advantageous in particular when, for example,
a frequency family of power amplifiers for mobile telephone base
stations must each be accommodated in housings of the same size.
With the method according to the invention for designing matching
networks, a practicable alternative is available for the first time
in 74 years. In particular, the method explained here renders
unnecessary the impedance inversion used heretofore.
[0533] FIG. 27 shows an electronic circuit, in particular for a
high-frequency signal. The circuit has a first source element
Q.sub.1, and a second source element Q.sub.2, and a first matching
network M.sub.1, and a second matching network M.sub.2.
[0534] The first matching network M.sub.1 and the second matching
network M.sub.2 are designed according to the exemplary embodiment
from FIG. 12.
[0535] The second source element Q.sub.2 is designed to output a
signal S with a center frequency f. The load L has a load impedance
Z.sub.L. The second matching network M.sub.2 has line-like series
elements L.sub.S1 . . . L.sub.S20 that carry the signal S.
[0536] In this case, either the line-like series elements L.sub.S1
. . . L.sub.S20 only have line impedances Z.sub.S1 . . . Z.sub.S20
less than the load impedance Z.sub.L, or a sum of the electrical
lengths of such line-like series elements L.sub.S1 . . . L.sub.S20,
each of which has a line impedance Z.sub.S1 . . . Z.sub.S20 greater
than the load impedance Z.sub.L, is less than one quarter of a
conducted wavelength .lamda. associated with the signal S. The
wavelength of a signal of a given frequency on one of the line-like
series elements L.sub.S1 . . . L.sub.S20 in this case depends on
the physical implementation of the relevant line-like series
elements L.sub.S1 . . . L.sub.S20.
[0537] Further exemplary embodiments of matching networks are shown
in FIG. 28ff. FIGS. 28 and 29 each show the matching structures
created on the drain side, which essentially represent the first
matching network M.sub.1 and the second matching network M.sub.2.
In this context, FIG. 28 shows a layout for a load-modulation
amplifier arrangement for an operating frequency von 1500 MHz and
(at the same scale) FIG. 29 shows a Doherty design for the same
operating frequency.
[0538] As is evident from FIG. 12, for example, the method
generally permits two solutions for pairs having a cyclic degree of
freedom associated with the peak amplifier branch and a cyclic
degree of freedom associated with the main amplifier branch.
Accordingly, the load-modulation amplifier arrangement encompasses
two disjoint solutions for the transforming action of the matching
networks M.sub.1, M.sub.2. Two matching networks associated with
these two transforming actions are shown to scale in FIGS. 28 and
29. The considerably smaller electrical length required for the
structures of the matching networks M.sub.1, M.sub.2 as compared to
the prior art is especially advantageous. In fact, for one and the
same desired transforming action, even with an identical estimate,
families of matching networks are to be determined, each of which
implement the desired transforming action. The structures differ
from family to family in their electrical lengths by multiples of a
half wavelength, however.
[0539] Structures of the matching network M.sub.1 are shown to
scale in FIG. 30 as exemplary embodiments. The structures are
determined according to the exemplary embodiments explained above,
and effect a mapping in the forward direction at 1500 MHz of the
first counter-image impedance of (10.1-j*11.0) .OMEGA. onto a first
image impedance of 4.OMEGA.. Moreover, the structures effect a
mapping in the forward direction of a second counter-image
impedance of 50.OMEGA. onto a second image impedance of
(1.44-J*3.5).OMEGA..
[0540] The structures in the examples in FIG. 30 include four
serial, homogenous microstriplines on a dielectric with a thickness
of 20 mil and a dielectric constant of 3.5. In FIG. 30, the end of
each structure facing the counter-image impedance is shown, while
the structure at the bottom has the desired image impedance.
[0541] If one numbers the four homogenous microstriplines in FIG.
30 at the counter-image side connection consecutively from 1 to 4,
the three matching structures have geometric lengths L and widths W
of:
TABLE-US-00001 W1 [mm]/L1 [mm] 6.467/26.173 1.098/14.913 16/5 W2
[mm]/L2 [mm] 9.973/48.424 2.850/39.098 1/2.927 W3 [mm]/L3 [mm]
6.424/52.078 12.383/14.547 16/1.126 W4 [mm]/L4 [mm] 14.5/3.5
14.5/3.5 14.5/3.5
[0542] Because of the electrical lengths of the new structures of
the matching networks M.sub.1, M.sub.2 in load-modulation
amplifiers that typically are shorter by a half wavelength as
compared to the prior art, the achievable relative bandwidth of the
matching structures increases from a typical value of 5% for
load-modulation amplifiers of the Doherty type to a typical value
of 13% for load-modulation amplifier arrangements according to the
two exemplary embodiments explained above.
[0543] The diagrams in FIG. 31 represent the transformation paths
for three structures of the matching networks M.sub.1, M.sub.2 from
FIG. 30 in Smith charts. The upper row shows the first
counter-image impedance and image impedance, the lower row shows
the second counter-image impedance and image impedance.
[0544] The invention being thus described, it will be obvious that
the same may be varied in many ways. Such variations are not to be
regarded as a departure from the spirit and scope of the invention,
and all such modifications as would be obvious to one skilled in
the art are to be included within the scope of the following
claims.
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